Your overall tax due will depend on your salary for the whole tax year. While you are working you will be taxed each pay period (may be monthly or weekly) on a "year to date" basis. Unfortunately the UK tax year starts in April (specifically on the 6th of April)
Lets assume you have had no other UK jobs in the tax year, that your employer has filed the correct paperwork with HMRC and your employer pays you three equal payments of £5000 late in July, August and September. In July you will pay relatively little tax (I make it about £166 assuming no pension contributions, possibly zero if you have pension contributions), because you will have have four months allowances to go at but in August and September you will pay significantly more (I make it about £800, again assuming no pension contributions). Assuming you do no further significant work in the tax year then this will represent a substantial overpayment of tax as in the end you should only pay about £500 for the tax year.
If you fill out tax returns this will be squared-up at tax return time, but most people in the UK don't have to fill out tax returns and while it's possible to opt-in to filling them out they tend to be a bit of a pain.
My approach in such circumstances (though with rather smaller amounts of money involved, congrats on the high-paid internship) was to wait until the tax year is over, then write a letter to HMRC outlining how much tax I had paid, how much I thought I should have paid and asking them to confirm my calculations and return the overpaid tax.
On top of the tax you will also have to pay national insurance, unlike income tax this is reckoned per pay period. So there won't be any refunds due. Expect to pay about £430 per month in NI.