Bit of advice - if you want the jobcentre to look at helping you with the cost of training, ask to book an interview with a personal advisor, the person who just signs you on is not trained to know the full range of training and provision available for everyone, and is unlikely to give you a helpful answer!
When you see the advisor it would be helpful to prepare in advance - provide details of the training you would like funded, the costs of such a course and a local provider with whom the course is available, and some details of why it would be especially useful for you - bring details of jobs it would enable you to apply for, that you'd stand a good chance of getting if you went on the course/took your qualification....
The advisor should then consider whether it is appropriate to make an application for funding via a process called Low Value Procurement (LVP) -accessing funding for training that is set aside through something called the Flexible Support Fund (FSF).
Basically for the advisor this involved doing some paperwork, essentially creating a business case, which is then sent off to the job centre district office to see if the training is worth funding, essentially they will decide on the evidence provided whether it is viable and worthwhile in terms of *significantly* boosting someones chances of finding work.
Be realistic - if you've never ever worked in IT, then they're unlikely to fund an industry level IT related course for you, but if theres something you'd like as an addition (perhaps a course you want to do as not having done it yet is holding you back from getting/applying for jobs you may otherwise get, as you already have some of the relevant skills, quals and experience) then it stands a fair chance...!
As an advisor at the job centre myself who has put together such applications for people...I have not yet had one turned down where in my own mind it was a worthwhile course and a realistic boost for that persons job prospects.
The reality of the labour market is considered too - you may struggle to get funding for a course or qualification in which there are very very few related jobs in the local area, unless you are demonstrating a willingness to look for work elsewhere and show consistent evidence of doing this.
If approved, you will do the course with whichever provider gets awarded the funding by the job centre (not necessarily your chosen provider or the one you got costs from). There is no guarantee of funding, its all on a discretionary basis, and there are some local differences based on area, but they can and do fund courses through the process I have given an overview of.
Now theres not funding for anyone to do a PHD or whatever, its simply not logical or affordable for the government to be funding really high grade and expensive qualifications all the time for people who are essentially job ready by virtue of already being qualified (and the bar by which the government considers people as 'job ready' is quite low, most 'basic skills' courses delivered/funded 'for' the job centre focus on people attaining Level 1 or sometimes level 2 numeracy and literacy, which is really quite basic when considered in the round).
It is worth noting that this process to fund training is not available for people who are on the Work Programme (or available for those on Flexible New Deal when that was still running) - in such instances all responsibility for funding is past onto the provider, essentially the job centre pays the provider to help you and its up the provider to decide how best to use any such funding.
