No, the UK Government provides grants for work done in the UK, whereas the EU provides grants for projects involving collaboration between several countries. Of course everyone recognises that some of the money has come from us in the first place: we put money into the EU pot, and we get money out of it. As WP points out, collaboration with EU isn't going to suddenly stop when we leave, but it is going to be a lot harder for our academics to get involved in these multi-national projects than if we were still members.
Regarding the observation that UK universities are doing much better in the league tables than those of any other EU country: that is one of the reasons that we have benefited so much from EU freedom of movement. Students and researchers from all over Europe come to our universities, paying their student fees and making their contributions to our economy. When we are out of the EU, they may as well go to the USA or anywhere else, especially with the Home Office's attitude of making it as hard as possible to get visas (which has already been making it difficult to recruit overseas students from non-EU countries).