I typically would suggest a "tracker" as an easier and less expensive way to get into this.
I don't know UK prices for these products, but in the USA, here are some sample prices:
1) The iOptron "SkyTracker" retails for roughly $300 USD. It was probably the most popular tracker ... until Sky Watcher came out with their model. The product works well, but the owners do have a few gripes about the system.
2) The Sky Watcher "Star Adventurer" has a base price of roughly $300 USD... but they sell two optional accessories and for astrophotography I'd _highly_ recommend both of them because they'll make life much easier. The first accessory is a "wedge" that allows you to have more fine adjustment control over the angle of the tracking head. The second accessory is a counterweight bar (with weight) that allows you to achieve neutral balance for your camera. With good balance, the motor wont struggle to track and you'll get more accurate tracking AND the system can handle heavier loads if you want to use a larger/heavier/longer focal length lens.
3) I own a Losmandy "StarLapse". Losmandy makes high-end mounts ... they are actually a machine shop. Nothing is mass-produced... it's machined to exceptional tolerances. I can't say there is zero plastic... but nearly everything is machined metal... there's almost no plastic parts. It's the highest quality tracker and handles the heaviest loads... but it's also the most expensive. It's about $700 USD and that does _not_ include the optional polar alignment scope (which I think is about another $300... while it is probably the nicest alignment scope I've ever used, it's also roughly the same price as a QHYCCD "PoleMaster" which is a digital alignment system that will do a faster and more accurate alignment job.
4) Vixen made a product called the "Polarie" sky tracker but I don't think they make it anymore. It was probably technically a slight step-down from the iOptron SkyTracker (and the two systems look nearly identical).
5) There's also a product (which I think is actually made in the UK if I recall) called the AstroTrac. The AstroTrac is basically a motorized barn-door wedge ... but made out of high quality machined materials. The downside is that it's very expensive (it costs as much as a StarLapse... but isn't nearly as good). It is versatile enough to take any single long-exposure. But if you wanted to collect a lot of data (imaging an object for... say 4-6 hours with of data on one object (which many imagers will do) then it would have to be repositioned (it has a limited travel unlike the other trackers which can rotate continuously through 360º and just keep going.)
In terms of price vs. quality... probably choice #2 is ideal for most people. The StarLapse is probably best in terms of quality and ultimate versatility (you can attach two StarLapse systems to each other to do two-axis tracking and the system handles the load) but it's also about twice the price and the Star Adventurer has helped owners produce a lot of exceptionally good results (stated differently: I doubt that if you bought a Star Adventurer system you would later regret it and wish you would have bought something better.)
Then there's the telescope mount route...
I don't think you'll be happy with this route for $2k price tag.
While you can ultimately do more with a telescope and quality mount, a "quality" mount starts at about $1500 USD. There are sub-$1000 mounts and they even have auto-guider ports... but their tracking quality isn't good for high quality imaging. This is not to say people haven't used them for this... they certainly have... with challenges that had to be overcome. Celestron, for example, makes an $800 USD mount called the "Advanced VX" mount (or just "AVX" for short). But imagers complain that it doesn't have proper bearings so it's tracking performance isn't as good... they complain of "stiction" problems. These problems are somewhat typical of the lowest cost mounts.
The mount quality becomes more important than the scope quality when you do astro-imaging. For "visual" astronomy, the scope quality tends to be more important than the mount... but not for imaging.
Then there's the scope price (because for $1500 you *just* get a mount... no scope).
BTW, the mount type really needs to be an equatorial mount. An alt-az type mount has a lot of challenges (great for visual... lousy for imaging). The field of view is _very_ slowly rotating in an alt-az mounted scope and that field rotation will blur the images and elongate the stars. You can put an alt-az scope on an "equatorial wedge" to fix the field rotation problem, but this causes other issues. The camera often wont have enough clearance to fit between the forks if the mount tries to point too close to the celestial pole (the camera will collide with the base if the forks aren't log enough) and you can get blind-spots near the southern horizon (for northern hemisphere observers). Lastly, it's more difficult to "balance" an alt/az scope (and you NEED good balance.)
At the low end of the spectrum is probably the Newtonian "Astrograph". An "astrograph" is an optical tube designed specifically for astro-imaging purposes and there are lots of different typescope types designated as "astrographs". So "astrograph" isn't really a scope type... it just means it is specifically optimized for imaging (vs. visual). You CAN use an astrograph for visual use too.
There are many other options...
"Achromatic" refractors are low cost but they have CA (Chromatic aberration) problems.
"Apochromatic" refractors are excellent... but they are _not_ low-cost scopes (typically not less than $1000 USD and often several thousand).
Compound scopes such as the very popular Schmidt-Cassegrain Design are also popular. These tend to have long focal lengths (and high focal ratios). So the downside is that you end up with a long imaging time, but the advantage is that they work well for small objects in the sky (well... small based on our point of view... all of these objects are huge if you were up close.)
As the focal lengths get longer, tracking becomes more of an issue. While you can get away with a reasonable duration exposure at, say, 500mm focal length... when you get to longer focal length scopes (an 8" diameter SCT would have a focal length of about 2000mm) you _need_ a guiding system. An auto-guider is typically a second camera and second scope (both on the same mount). The guide camera takes images roughly every few seconds and compares a selected star's position in the image relatively to the first image it took... and will send corrections to the mount if that star appears to be drifting out of position. This allows you to take very long exposures with the main imaging camera with no smear due to tracking errors.
There are lots of options ... but the costs and complexity is certainly higher with a quality telescope mount and imaging scope(s).
While I think most people do try to start out on a reasonable budget, they start to realize which components need to be beefed up for better performance and it doesn't take long before you exceed $3k... or $5k... or $10k. I'm not kidding about these prices... _most_ serious imagers that I know (people who really enjoy taking astro-images so they take many images per year) ultimately kept upgrading their gear and nearly every imager I know has probably spent more than $10k on their gear (very few people spend that all at once... but many of them work their way to that expense by realizing they need a better mount... a better guide camera... a better scope... and the next thing you know they've sunk a lot of money into the hobby.
Unless you're ready to commit a good chunk of money into the hobby... I'd probably encourage you to go the tracker route. It's much less expensive and much easier to learn. But you'll primarily be taking lower focal length (wider pieces of sky) in your images when you use a tracker.
BTW, stability is king no matter what route you go. So even if you get a tracker... you'll want a rock-solid tripod... nothing wimpy (this is the one time where you don't care how much it weighs... it MUST be solid. You wont be carrying it around all day like a tourist... so don't worry about how much it weighs.)
