I'm sorry for your loss. An application for housing benefit might allow them to stay in the rented home this summer if you can't take them in. They may both be able to claim benefit for the summer if they don't have jobs.
p.s. at the uni I know best, applications for bursaries close imminently so really important to do this now for your nephew - I realise this will probably be the last thing on his mind but it might be worth helping him with this specifically.
Many universities have hardship funds for children in unexpected situations. Please encourage your niece to speak to her personal tutor (or equivalent) as soon as possible and s/he is likely to give plenty of support in linking up with the student financing people. Your nephew might be in a different position and able to apply to other 'needs based' bursaries. These are different at each university and generally require completion of a lengthy application form but the university will be able to advise. There is usually a section on each university's website with information about scholarship/bursary assistance and/or hardship funds.
So sorry - what a terrible thing to happen to your niece and nephew at this stage of life.
They will be assessed as being independent students, so they will get full student finance (currently £7177, from memory), plus the normal low income bursary from the university (details of which can be found on the university website.
They will both have to contact student finance, and should expect to be asked for proof in the form of a death certificate. Therefore, multiple copies of the death certificate should be ordered (one each for SF, plus others as necessary).
The university should probably be made aware, as they can put pastoral support into place for them. If academic results are affected, then it will help to put those into context; bereavement counselling is quite probably on offer; from an accommodation point of view they may be able to help them over the summer if other can't; Access to Learning bursaries are available if they end up financially up the creek without a paddle.
So sorry for your loss. What a terrible thing to happen...
In terms of support I would contact the university directly in the first instance, there should be some sort of student support department who can advise you on finances and get the ball rolling for whatever applications are needed.
Sadly my sister died on Monday unexpectedly, leaving my niece who is 19 and currently in her 1st year of uni and my nephew who is hoping to start uni in September. I wondered if anyone knew about any particular support for children with no parents and no financial help? (My sister rented and was in lots of debt so there will be no savings to pass on to them)
I've done some googling but can't find anything, and I'm wondering if it's down to the specific uni's?
Would appreciate any help in guiding me through this!