You are connected to different equipment at the exchange end from your former LLU service using different jumper wires to before. Sometimes you get a particularly good combination of equipment and line conditions, which performs better than expected, sometimes the opposite happens and you get an underperforming combination.
As you've gone to PlusNet via Sky, and had a fault repaired whilst on Sky that might have led to part of your line being swapped for a different pair of wires, there's really no way to know precisely what the root cause of the slower speed is, especially without detailed diagnostic information from the O2 setup to compare to what you have now (attenuation figures at a minimum, detailed information on bin SNR and bit loading would be of interest). Any PlusNet / BT Wholesale speed estimates might have been based on a line with better parameters than the one you have now - but there's no way to go on a 'shopping expedition' for a better pair or return to your original pair if part of your line was swapped for a different pair.
If your PlusNet connection is sufficiently stable, it may eventually find its way to a 3dB noise margin by itself, which should improve the connection speed. Beyond that, I'm afraid an estimate is an educated guess and no more. A speed lower than the estimate is not grounds for escaping from your contractual obligations, though PlusNet have the discretion to release you should they wish to.
As the Be/O2 residential network is closing, you've just left Sky and seemingly don't want to go back and any BT Wholesale based ISP is likely to perform similarly if not identically to PlusNet (they use the same equipment, and you will remain connected to the same DSLAM port if you migrate from one BT Wholesale based ISP directly to another), that doesn't leave many options.
SamKnows gives the remaining options as AOL, C&W, TalkTalk and Tiscali, but quite apart from this data not necessarily being up to date, it's also misleading. Both AOL UK and Tiscali UK's operations have long since been taken over by TalkTalk, so those three are only actually one option for new customers (and I very much doubt there are still three separate networks after all this time). What's listed as C&W is the old Bulldog network, which still used as a wholesale provider for certain connections (
ADSL24 still lists a C&W based product, I'm not sure if any other ISPs still sell a C&W based product).
Rather than looking to escape from your PlusNet contract and move to one of the two remaining ADSL options, which could turn out to be even worse, what does the
BT Wholesale checker list against your phone number for FTTC? It seems that at least some parts of your exchange area may have FTTC deployment to come in the next few months, which could offer you significantly faster speeds with, as I understand it, no need to buy yourself out of your PlusNet ADSL contract if you upgrade to PlusNet Fibre.
Meanwhile, it would seem a good idea to follow the suggestions you're being given by RobertoS about bringing your case to PlusNet's attention.