For your £300 budget I can only agree that the TAU 7 ( even better if you can find a genuine TAU 7 Match) is an excellent choice and a Steyr LP1 or LP1P for a little more is at least as good as the current ( and far more expensive) Steyr LP10.
The mentioned CO2 pistols from Feinwerkbau ( Model 2, C10 and C20) and Walther ( CP1, CP2 onwards....) are superbly engineered pistols that some of our club members actually prefer to the PCP pistols and everyone that shoots them likes them and finds them rather more "forgiving" that the PCP pistols to shoot.
We have one excellent Alpha in our club that has proven to be very accurate and reliable but this one is "the exception and not the rule" as the others have been unreliable from new and been very disappointing so I would suggest looking elsewhere .
Rossendale Target Shooting Club. Every Tuesday and Thursday evening 7 - 10pm.