Without asking any legal advice at this stage. I was thinking with my partner whether it would be best and less time consuming and probably a better investment if both married this year in London. As a British Citizen and in a long and committed relationship since 2012 with my partner who is a EU Citizen; we thought that maybe marriage will simply resolve all those legal issues in relation to her right to remain in the UK after Brexit. Can I marry as a British Citizen to a EU Citizen so that my partner can get the right to live with me here in the UK? (no sham marriage)
At the moment, there is no way to know for sure what rules will apply when the UK leaves the European Union. In fact, according to media reports from the last couple of days, what will happen to citizens from other EU countries currently living in the UK and to Britons living elsewhere in the EU is shaping up to become one of the major issues in the upcoming negotiations.
That said, I cannot really see how marrying could weaken your position. In general, the right to live with your family is strongly protected (this is actually enshrined in article 8 of the European Convention on Human Rights, which is completely unrelated to the EU). It's also possible to come to the UK on the basis of a stable relationship but it's always somewhat easier if you are married.
Furthermore, marrying now can also be advantageous. If you have been married for several years whenever the issue comes up, it will be more difficult to dismiss your marriage as a sham marriage designed to game the visa or residence system (although being able to document that you have effectively been in a relationship or lived together for several years is always required and would also be a strong argument without being married so think about that too!).
However, being married does not immediately "solve" all issues. The UK is among the most restrictive countries in Europe in that respect and gaining the right to stay in the UK for third-country (i.e. non-EU) citizens involves quite a bit of paperwork, not insignificant fees and meeting other requirements (minimum income, knowledge of English). In fact, this system is so restrictive compared to EU law that it's become common to use the latter to circumvent it.
In summary: It's possible to sponsor one's spouse visa or residence permit and that's why marrying might be useful to secure his or her right to stay in the UK but it's not as easy as the current regime for EU citizens.