^ It depends on a number of different things, it is very much preferable that you are a still a student to do an unpaid internship in London, because they cannot hire graduates without paying them.
Your portfolio is important, the work you have done, and to convey your capabilities and what you could bring to the company.
For example, if you applying to Mary Katrantzou a high level of interest, a high level of capability and experience in digital printing would get you noticed, I am sure.
You will almost certainly be interviewed, I have interviewed at two different brands in the past, in remote parts of London, I think it's very rare for brands to cover travel expenses. Different brands will require different things (aside from your portfolio), for example, I was asked to bring an example of my sewing skills, I have heard of others being asked to do small projects to bring with them.
As with all internships you also must be aware that you aren't necessarily going to be doing the most creative things, the interns there will all be fashion students or designers but will still have to do menial tasks like photocopying, flat drawings, fetching coffee, etc.
You are there for whatever experience you can gain out of it and at the end of the day you will have 'Intern at Mary Katrantzou' or whatever on your C.V. which will be a boost for your future endeavors.
Indeed, I interned at a London brand only for one week one season and another week the next season and all I did was hand-sew and run errands; often the brands are small and just need the extra hands to work for them without having to pay them.
It seems very strange, and can be expensive (especially in London) but you meet great people and gain experience which is so necessary to further yourself in fashion.