One thing that's helped me when it comes to saving money is to drink only water. So say take two months and don't have tea, coffee, soft drinks, fizzy can drinks, alcohol, anything like that. Then save the money you would've spent. It's a good way of getting a few pounds.
I'd start small so say look at 2 nights away in a Travelodge, in a location in England or Wales. In advance, trains can be booked up with big savings - for example I went to London for £7.50 on Virgin trains, when if you turn up on the day it's £50. Have your spending money to be what you'd normally spend but maybe with one meal out. If you chose the right places you can get main meals for £5.
It might take ages to save up for this, but it's a good goal if it's what you want. I went to Rhyl on holiday for less than £100. I have happy memories of it. All the things I did were free or cheap really like the beach and (back then when my health was good) walking around and then going to a cafe. But it was a holiday. It seems like it is really important to you, so I'd try to work towards it. Yes, the situation really sucks with not being able to afford one.
One thing that might help is use an energy switcher. In May, a lot of people got switched to standard tarifs as their contracts ended and it's been one of the biggest increases in recent history. Gas and electricity is an area you can potentially save a lot on. Or things like look into your toilets - 30% of water bill is usually flushing. If they're not dual flush look at one of those water savers/brick things, which can save quite a lot per year. Shower heads that save £s per year. LED lights - some of them are around 10% of the electricity in old fashioned incandescent lights. See if you're on the cheapest tarif for internet. With mobile phones, look into SIM only contracts. I went to SIM only and when I've worked it out over a 2 year period, I've saved hundreds. Really, hundreds. Yes I have a shit handset but at least I'm not paying £40 a month. Can you shop in a different supermarket and make savings there? Or get all household items/cleaning products in somewhere like Poundland. I've made mad savings sometimes like I found a baby soap for 35p so use that instead of the one I had before that was over £1. And I found 10 washing up sponges for 40p when before I was buying 2 for £1. Buy in bulk when an offer is on - e.g. if you see something half price, look at when they expire, and get a lot of them, even if it's a lot of money you save long term.
Good luck and I hope you get what you want.