As posted above, a PP did it with success this year, but it's not guaranteed. We considered it a couple of years ago but were advised against it both here and on Snowheads. Whilst I was looking into it, I found it wasn't as much of a budget option as you'd think. Lift pass prices were on par with what you'd pay in the Alps, and for a significantly smaller area, with no snow guarantee, we didn't feel they were good value.
In terms of transport costs, we drove to Les Arcs over Easter. Fuel, tunnel, and tolls came in around £450 return. There's 4 of us, so just over £100 a head, which is cheaper than flying + transfer.
I just looked at the trainline, and for the 4 of us to go from Temple Meads to Aviemore is £815 for an Open Return or £742 to have a timed ticketed return in May half term (chosen to be comparable to February half term).
The train takes 10.5 hours and requires 3 changes. To compare, it was 14 hours door to door for us to drive to Les Arcs, and that was to guaranteed snow (we live in your neck of the woods, so similar drive times).
GoCompare estimates fuel each way to be £52 in my car, but my husbands is more expensive, so that could change for you, and Googlemaps says 8 hours. So driving will keep the budget down more than the train.
Have you looked at Sunweb? There's some great value options there. Alternatively, directly booking your accommodation. Our 2 bed apartment in Les Arcs for the first week of Easter was £368 via Vrbo. It was less than a 5 minute walk to all the lifts. That was an unusual find, though. Most sit around £500+ for the week (which for school holidays is still excellent).
It is possible to go to Europe to ski on a budget if you're savvy about it.