EU Spouse Visas
UK immigration at present is a little difficult. The idea of being refused a visa as they maybe a burden on the public purse is a shame. I assume you are both working and the funds are not an issue as suggested. I would recommend you look at inviting your common-law wife to the UK as your E.U partner. The burden of proof regarding funds available under EU law is less than the UK immigration requirements.
In short apply under EU law to bring her as your partner, assuming you have been living together. If not, as an appeal is out of the question it would be advisable to focus on her Greek citizenship rather than throwing more money at the UK Visa just for another rejection. let me know your thoughts and I would be happy to assist you with your visa.