Been skiing 25 years now. It's not possible to go for a week for £400 including spending money and passes.
Passes are very expensive in many European resorts, so scope these out first. Don't go to France or Switzerland, they are more expensive than Austria and Italy. You might find a small local resort that is cheap, but you won't find many Brits. I know of one or two near Grenoble, but they so small that they are half day resorts for an experienced skier. This size of resort could be OK for you, but it could be limiting when conditions are poor. With a larger resort, you get the option to go higher/lower, or just elsewhere, to get the best conditions depending on the weather/temps.
As a beginner, don't pick a super resort (several valleys and a large ski area). All you will do is waste money on an expensive pass and an extensive area that you won't be able to access.
Many resorts have free lifts on the nursery slopes. These will suffice for the first day or two, saving you 30-50 Euros. So don't buy a week's pass when you arrive, buy your pass when you are ready. Selva Gardena and Canazei in Italy's Sella Ronda have huge easy nursery slopes. The lift for this was free when I last went there and a member of our party spent the best part of a week learning to board on these slopes.
Pick somewhere with lots of easy gradients and give yourself a chance, but my snowboarding mate reckons he prefers the steep stuff because it's easier getting up after a fall. I dunno about that, but then i'm a skier.
The other thing you need to avoid is resorts with a lot of level(ish) tracks, unless you like walking. You'll be frustrated by all the skiers polling past you.
Andora is probably your best bet. Much cheaper than the usual popular destinations. You can get full board packages including passes for close to you budget if you pick the right moment to book.
Go early/late in the season. Check resort websites to get tariffs, but expect a shorter ski day at the beginning of the season and slush at the end. Snow cover is potentially an issue, although the late season is frequently much better than people imagine.
I haven't been to Slovakia or Bulgaria, but from what i've heard, it is cheap and basic. Lifts aren't great and these resorts fall below par. Again, this is not such an issue to a beginner.
If you want a reliable source of information on ski resorts worldwide, you must buy a book titled "Where To Ski". There is also a website if you google it. This reference has been spot on accurate for me every time i've used it in the past seven years.
Make sure you always wear a helmet and proper wrist guards!