Tricky!
The way I see it, you have two options - a new bag or (and I hate the word!) a sleep "system".
As
@MichaelW2 says, for those temps there is a weight/volume penalty for synthetic. I'm not sure of the UK market, but I can't see too many decent down bags for your budget?
As for a "system" what do you sleep on? An emergency blanket (silver or gold) can be a way of boosting the mat insulation for a few quid.
A second bag for inside or outside your existing bag would add a season or two as would a "thermal" liner. Or a bivi bag. Of course, that adds weight and volume.
There's also the clothing you wear to consider.
I experimented with a synthetic Vango of similar specs to yours. I tried it out with a merino wool liner inside and a goretex bivi outside down to -8. I survived!
I found the merino too fragile to use longterm as a liner. Any thermal liner I saw seemed very flimsy too. If I was to try that again, I'd opt for a cheap down bag inside the Vango.
One thing to bear in mind if buying a new bag is that prices vary depending on the time of year. Always a good idea to have an idea of what you might like and track the prices. You can save yourself a bit.