Welcome to the forum
It will depend on whether the individual universities are still taking any applications and if they have any places left on the courses you want to apply for, so you'd be best contacting the relevant academic departments of the universities you are interested in and asking them.
I think your main problem will be that if you are American and need a Tier 4 student visa, there probably won't be enough time to apply for and receive the visa in time to start the course in September - as you normally need to allow at least 3 months for the paperwork to be sorted and to complete the application process (https://www.gov.uk/tier-4-general-visa/overview
In order to get a student visa, you need:
- a Confirmation of Acceptance for Studies (CAS) from the university you have been accepted to, specifying the course you have been accepted on and that you meet the points requirement for the visa. I believe these are only issued once a month and it may take several weeks for them to apply for it and for you to receive it
- to be able to show you have enough money to pay for the first year of tuition for the course plus the required living costs (so about £25,000 in total). This money must either have been in your personal bank account in full for a minimum of 28 days before you apply for the visa, or you must have evidence of an approved US loan (which is accepted by the UK university).
Then once you have this sorted out, the actual visa can take anywhere from a couple of weeks to a couple of months to be issued once you have mailed the visa application to NYC for processing - depends how busy the consulate is. In June 2015, they were processing 57% of student visas in 2 weeks, 97% in 3 weeks and 99% in 6 weeks, but this processing time can increase dramatically in July and August due to the sheer number of applications received.
Most people who wish to attend a UK university in September will apply for the course at least 6 months in advance, then they will receive their CAS from the university in May or June. They will apply for their visa in June or July, receive their visa in July or August and then move to the UK in August or September (you can enter the UK on the student visa up to 30 days before the course start date).
In general, January start dates are uncommon in the UK because for the most part, courses require you to register for an entire year at a time (not individual semesters), and most masters courses run for a full 12-months (or sometimes 2 years) from September to September, with everyone starting and finishing at the same time.
So, if you are too late to apply for a course and get a visa before September 2015, you may well have to wait until September 2016 to start a course.