Asking to drop her rent down to £300 AND the BF staying over 2-3 nights a week is taking the piss.
back of an envelop calculations........Assuming she works full time and is qualified, she'll be on circa £30k pa, that's about £23,800 pa and then there'll be her student loan of £720pa, so that's £23k roughly speaking, £1900 per month. And she wants to pay £300 rent. I'd want to see her saving £1k a month, no ifs, no buts, and she's still have £600 per month spending money. OK there may be travel costs.
I'd want to see her saving £12k a year. And I'd want to know the BF was pulling his weight in the savings effort too. Kent isn't a cheap county to buy in - how much deposit are they looking for ?
I would be tempted to offer £400 rent per month - but and it's a big but, she has to prove she's saving and saving hard. And at the first suggestion she's no (eg big holidays, lots of nights out) back full on £500.
As you are nearly retired, your income will be going down. Probably more than you bargained for as you've dropped your hours from full time. Another employed adult in the house may effect your ability to claim benefits - please don't forget this.