Bear in mind that not all grey imports are the same deal.
A great deal depends on where you buy it, and what is included. There have been two main points raised above, legality and warranty. The main legal issue is have the taxes been paid on it when imported. This is especially critical if you are buying from a dealer that purports to be a UK dealer but only has a postal address here (Usually a PO box which is just a letter drop and forwarding service). These outfits tend to hide the fact that they are not physically in the UK and will send your camera from outside the country. That leaves you liable for the taxes when it arrives and, whilst you may be lucky and not be charged anything, you could find a bill for 20%+ arrives first, which you must pay if you want the camera delivered.
The other issue is warranty. If the camera is sourced from another market (such as Hong Kong) then that is where the original warranty will be based. Therefore if work needs doing you need to send it back to HK, or wherever, or pay to have it done locally.
However, not all grey import dealers leave you to take these risks. The reputable ones import the cameras, pay the taxes and provide you with a local warranty. They aren't as cheap as the less accomodating sellers, but cheaper than a regular main dealer. One dealer who gets very good recommendations from many people on here, and I have bought from them myself, is HDEW. They started as a small chain of bricks and mortar camera stores but, with the coming of the internet, switched to online selling from a main base. They provide grey imports but the gear has all taxes paid on it and you can go in and buy it over the counter if you wish. So, there are no legal issues, the gear is as legitimate as anything else bought from a UK dealer.
As for warranty, they provide a three year warranty on bodies, as opposed to the standard one year warranty. In theory, you need to arrange work through them and they get it done at an official Canon service centre in the UK. So, no different than a non grey item apart from going through the third party warranty. I have seen several people who have said that Canon have accepted the cameras directly, within the first twelve months, and they say they were told that as the cameras were sold by a UK dealer with a VAT receipt, they will cover them. I cannot personally verify that though, as my 5DIII I bought through HDEW has never faltered in the two years I have had it. Obviously, you would need the third party warranty in years 2 & 3, but that is because the standard warranty would have run out.
Before I purchased from HDEW I researched them carefully. All I could find was happy reviews and happy customers. When problems did occur (as they will with any dealer) they were sorted quickly and to the customers satisfaction.
They can't match the £624 price you were looking at, but that 70D / 18-55 IS STM kit is £779 on their site, compared to around £859 (£959 less £100 cashback) from an official UK source. Less of a saving but still worth having, and of course you get the extra two years warranty as well. I suspect that anybody selling the kit as low as £624 is selling gear without the tax paid and without a decent warranty.
(I have assumed that you are in the UK, as you quoted a price in sterling)