All networks will have blackspots somewhere, 3G on 2100 MHz has aways been problematic for all the operators, especially for indoor coverage.
If you are about to change contract on O2 get yourself a new mobile with UMTS900 capability. The Iphone 4GS and most new smartphones now have this extra band. UMTS900 propagates better than 3G on 2100 MHz and penetrates buildings better. O2 have already completed a lot of their UMTS900 coverage on Wirral and you will find very few "holes" in there coverage if you compare their coverage on here: http://www.o2.co.uk/coveragechecker
Enter your postcode and handset, if you select a UMTS900 capable handset you should see a big improvement in coverage for mobile internet and mobile broadband.