It's quite complicated and ever-changing. Higher Education (mostly universities) used to be free for UK citizens to attend. That changed in 1998, when they started charging fees of up to £1,000 a year. That was increased to £3,000 in 2004, and (controversially!) to £9,000 in 2010. That last increase led to nationwide protests, not just because of the sheer size of the increase, but also because the government at the time was comprised of a coalition between the Conservatives and the Liberal Democrats, the latter of which had made a campaign promise not to raise tuition fees. This said, most students receive grants and loans from the government to cover this (and some living costs) while at university, and repayment is tied to the amount you earn after leaving university. Currently, if you make less than £25,725 a year, you are not required to make any contributions towards paying off your loan. If you earn more than that, you need to contribute 9% of your earnings - for most people, that is deducted from their paycheck (the same way we pay our income tax and National Insurance contributions).
All of this is made more complicated by the fact that the UK is actually a country made up of 4 countries, and some of them have devolved powers (for example, Scotland gets to govern its own education, healthcare, and transport). Because of this, Scottish students at Scottish universities receive grants from the Scottish government to cover their tuition fees (currently £1,820) which do not have to be repaid (note: this applies only for your first undergraduate degree). EU students in Scotland also received this treatment, and have been able to attend Scottish universities without having to pay any tuition fees themselves, though this is due to change. Controversially, English students studying in Scotland were required to pay much higher fees (£6,750) per year, which they could borrow from the UK government through the Student Loans Company as stated above.
Basically, each of the 4 UK countries have different systems that make university tuition fees here awfully complicated. For the sake of Lydia though, she was an English student who attended an English university and therefore has an obligation to pay back the money she was loaned for her tuition if she earns more than the threshold for repayment (currently £25,725 per year).