I want to apply for LLM in shipping law can anyone suggest the best universities in UK

That’s a good question that which is the best universities. Universities come up in my mind at the moment are South Hampton and Swansea. However, don’t forget to look at other universities as well. 

Depends what you mean by «best», as the answer would be depend on what is most important to you, e.g. general uni reputation, maritime reputation, module diversity, teaching, networkong, location, etc. Swansea and Southampton are probably the best known maritime law unis in the UK at present. Southampton would have had a clear edge years ago before many of their profs either retired or spread around elsewhere, but the reputation of universities tend to be rather undynamic in the legal world. Swansea’s LLM might therefore not be as well-known outside of the UK as Southampton’s,  but Swansea seems to have established itself well enough with the UK shipping industry. UCL and QMUL also have their maritime or shipping law LLMs now, and there are undeniably some perks with studying in London if you are looking for a job there after your studies. The QMUL LLM should be more established than the UCL one and I think it also offers more maritme subjects. You’ll generally have more maritime subjects on offer in Soton/Swansea, while the two london unis will more likely require you to take other subjects to meet the degree requirements.