Regardless of the fact that, this contract does not, to my reading (IANAL), support their position that they have a claim over the UK-produced vaccines: pursuing a legal resolution seems silly because getting a judgement in your favour will take weeks or months. That is far too long for the timelines the EU wants.
Then, even if such a judgment is forthcoming - you still aren't that much closer to getting more doses because as any solicitor will tell you, possession is nine tenths of the law and the doses are in the UK. There is no realistic chance of any export occurring without the approval of the UK government. The UK has a very serious outbreak of coronavirus too.
Instead of getting on their high horse and starting an enormous public row why don't the EU: a) recognise that this is one of many vaccines and that perhaps, while important, is not singularly important to the effort b) make an arrangement with the UK government to have some kind of expedited access to vaccines? The UK will soon have a surplus of vaccines (and in fact has extra stock already by some accounts - people are being given unused doses). There is an existing trade issue that is causing problems for the UK that I am sure that the UK would like to get sorted...
This kind of over-legalistic attitude is how the EU got into this hole in the first place. Waiting for a single purchase agreement was a mistake because the vaccines have (mostly) turned out to be extremely cheap and the fact that many companies are working on vaccines likely means that none will be able to charge over the odds.