I am a mature student who has just completed an Access course, and has a confirmed place at the LSE for next year in the Government department.
Apart from the core modules (done by all students), I did optional modules in English Literature, History and Government & Politics.
If I share my experiences with you rather than offer advice, it may be of help to you.
I have found that an access course is taken seriously by universities, and they do indeed welcome mature students.
I chose the Access course because it was one year and offered to instruct me in areas I thought I might be weak on, namely essay writing. All of the teachers I dealt with were passionate about getting access students into universities, and were without exception helpful. Many of them also taught the A level students, and they commented that the Access students were often better prepared for life at university.
I applied to my 5 choices through UCAS unsure what would happen and waited. I got 2 offers from my 4th and 5th choices fairly quickly. Then I got two invitations for interview and an invitation to sit an exam at the LSE. Both of the interviews followed a similar pattern, with questions on what I had done since leaving school and on what I had learnt from those experiences. They were in fact asking questions which resulted from my personal statement. They then probed to enable me to show my enthusiasm for the subject, before finishing with a few mildly awkward ones to see how I reacted. The exam past paper is available on the LSE web site.
The route into university for a mature student is different from those who apply at 18. You have different things to offer and these are often as important as your subjects and grades. You have work and life experiences that can often give you an advantage, and the extra few years you have often means you are more mature and this perhaps shows in your attitude to your studies.
What I would suggest to you is that entry to university is highly competitive, and the degree you choose as well as the university has a major influence on the likely chance you have of getting in. I would suggest further that it is a lottery, in which there are very few first prizes and most people walk away without them. I was lucky. I saw plenty of evidence of friends on my course that were not. Too many of them (particularly in Law) applied to only the most popular universities, and as a result got 4 rejections.
I do not believe there is a “best route”. I believe there is what works best for you, and prepares you best for the process. I would pick 5 universities and talk to the admissions departments of each of them. I would talk to the departments which offer both the A level and Access course and ask them about their track records in getting students into university. I would get a feel for all the institutions you are talking too. I would visit as many as you can get to see how you feel about the place. I loved my college, and was comfortable there for the entire year. One of the universities I visited which was high on my list I just didn’t like, and would probably been miserable there for 3 years.
The LSE is reputed to have more candidates for each vacancy than any other university in the world. I would urge you to apply, but I would also urge you to consider a plan B. I wish you every success in your journey, although only a short way on it myself, I have enjoyed what I have experienced, and am eagerly looking forward to the challenges of the future.