Differences between International Relations and International Politics?

There is no difference, it is the same degree with a slightly different name. LSE, UCL and KCL are the best places for this subject in London.

There must be a very slight difference. IR must have more of a focus on foreign policy and supranational bodies. While IP must look at individual democracies and governmental systems more.

Obviously there's crossover though.

All degrees are slightly different from one another even if they share the same name, no one IR degree will be the same. International Politics is just another name for IR, some universities use it and some don't. Aberystwyth is very famous for IR, but they call their degree 'International Politics'. You should not make judgements about a degree's module content from the name alone.

It is very hard to get into those unis (LSE, UCL etc.) could you recommend others with lower entry requirements which are still good in this subject?

UCL don't actually do International Relations, they do PPE and Politics and East European Studies. SOAS if you want to focus on African or Middle Eastern Studies and don't mind the extreme left wing environment there, otherwise you need to start looking outside London to find other universities with good IR departments. Of the other univeristies in London, Queen Mary is fairly well ranked overall but not known for IR, Goldsmiths is good for Media and the other universities are mostly mediocre to poor.

UCL don't actually do International Relations, they do PPE and Politics and East European Studies. SOAS if you want to focus on African or Middle Eastern Studies and don't mind the extreme left wing environment there, otherwise you need to start looking outside London to find other universities with good IR departments. Of the other univeristies in London, Queen Mary is fairly well ranked overall but not known for IR, Goldsmiths is good for Media and the other universities are mostly mediocre to poor.

Only London (or other unis close to it) come into question now. What about City (they have International Politics)?

Why so limiting? City is ranked fairly well overall but not known for IR or IP.

Because I have relatives living there (I'm from Hungary). And what about Middlesex, is it a uni to avoid? It is ranked around 80 but it looks okay to me.