Sorry to hear your DF had a stroke, that must be stressful. I can see little things here you could save on. If you were desperate.
Your rent includes Sky TV but you also pay Netflix subscription. Ditch Netflix, and find a relative or generous friend who will let you piggy back on their account, or give it up altogether.
Also your rent includes heating presumably gas but not electric. So you aren’t in control of the gas, right? Can you get your gas and electric on dual fuel, it is usually cheaper, and get control of the account yourself? If that’s not possible, can you at least work with your family to help them switch annually to the cheapest deal possible. Program your thermostat so the heating comes on 30mins before you are home from work and before you wake up in the mornings in winter, and try and minimise the time it is on for. Also turn your hot water thermostat down - often it is set very hot and you can cope with it being somewhat cooler.
Are you paying TV license? Could you give up BBC and just use Sky, it is possible to live without it!
Could you break your phone contract or when it runs out, get your phone SIM onto the Sky account and pay it with the rent? I’m with them, 2gb data a month for £6.99 sim only, and any data I don’t use is banked, forever. They do 1gb deals too, I think?
Definitely still get married, but keep it very lean. Being really savage you might reduce the costs a lot, as you have indicated. What is left in that reduced £3k budget, maybe there is more you could strip out?
Your car - what do you drive? £27 a month for road tax seems high, mine is £20 a year (I appreciate I have a nice modern car, just seems like you must be driving an old tank or something!). I realise the car is essential, but trading in for a very small, cheap run-around might be better in the long run. Alternatively can you set aside savings each month now so you pay the tax annually rather than monthly? It saves a bit, and every penny counts.
When you shop for your new wardrobe, go second hand. When you are at a loose end not watching Netflix or BBC, get familiar with the second hand market on FB, Shpock, Vinted, Depop, eBay. So then you will know a bargain when you see it.
That phrase, “I don’t spend much on clothes… “ means what, exactly? This year I have bought a pack of 5 pairs of knickers and 10 pairs of socks as mine were too thin and in holes. I bought a pair of jeans in Primark, £5.99 as I had worn holes in my old ones. And I bought a pair of summer trainers for £4.99 in a sale, plus p&p but that was shared with shoes I bought at the same time for my kids. It is possible to almos eradicate your new clothes budget, next year I’m aiming for a zero spend.
Small things count. Stop buying brands, go own brand wherever you can is obvious, as you shop in Aldi already. But even there you can cut down - buy less meat, buy local in season fruit and veg.
Cleaning. Invest in a pack of 15 different colour microfibre cloths. Use them to clean with (dampen very slightly with after), you’ll save a lot of cleaning product. Stop buying paper kitchen towel, use the cloths instead, etc.
What do you spend on cosmetics? Can you cut down? Switch to bar soap in the bathroom as liquid soap is a rip off.
How about snacks? A bag of apples and a bag of carrots is a cheap and healthy way to fund snacks, avoiding crisps and chocolate.
Do you drink alcohol? Stop if you do.
Join a library - there are library online services too for free audiobooks and downloadable books - so you don’t need to ever buy books.
Agree with friends and family to have a no-adults-gifts policy for Christmas or birthdays, or limit the spend to a token amount.
There are loads of tips on money saving sites, read and absorb.
Regarding food it’s your partner, that seems weird - you don’t at the same things, or together? If one of you is turning the oven on to cook, it’s bonkers to only cook for one, so think about that side of things.