Check how it is paid... I did my PhD at 2 institutions as my supervisor got promoted as I went into 3rd year. In my first institution I was paid monthly which was easy but in my 2nd I was paid quarterly which was a pain when budgeting.
I know it's tax free, I'm comparing the stipend to my post-tax salary which seems the most sensible comparison?
Good point on NI contributions, need to look into that as I'm already missing years due to working abroad. Own a house and live with my partner and our council has scrapped single person discount from April this year so that doesn't apply. No children.
You may have initial trouble renting if places say "no students", but if you ask the landlord or get agency to explain you are graduates working for doctorates, it should be ok - though if someone in the house isn't a student, then the house is liable for council tax.
You won't get those years counting towards your state pension unless you work a bit extra and probably pay extra NI contributions.
You don't pay council tax if you are the only adult in the property. If you live with one other adult, the pair of you get a discount on council tax. You can also get discounts on travel expenses - a student railcard is 1/3 off the full price (though you can't always travel during peak time). These things might help?