While the European Parliament is a good route to go down if you want to lobby or raise awareness at the legislative level, most of the important policy development happens within the Commission, which is comparatively more powerful than the UK government. Because of the focus on consensus-building, policy put forward by the Commission, under the direction of the European Council, faces less party-political opposition in Parliament. If you want your research to inform current EU policy, developing a relationship with the relevant Commissioner and Directorate-General is the most effective route.
Your first contact should be the Commissioner (or their advisors) who is responsible for the most relevant Directorate-General. You may also want to contact the Director-General (analogous to the Permanent Secretary of State). You can find contact details on the Commission website, but it may be easier to seek the assistance of the UK Representation, who will be able to point you in the right direction, and maybe able to arrange introductory meetings to relevant Commission representatives: remember that you should be looking to develop an ongoing relationship with the Directorate-General staff.
It is also important to bear in mind that you should in the first instance contact the Commissioner responsible for the relevant area, not the UK Commissioner: Commissioners must act in the best interests of the EU as a whole, and should not advocate on behalf of their own nation’s interests. The current UK Commissioner, Jonathan Hill, leads the DG for Financial Stability, Financial Services and Capital Markets Union, so you shouldn’t contact him or his staff unless your research was relevant to that portfolio.
However, it’s worth knowing where there are British staff working in the Commission. Commission staff are politically neutral, and like the Commissioners must not advocate on behalf of their own nation’s interests, but they can be useful sources of information and informal advice.