What can I do?

mart.vader

As the LL is going to be away, it's far easier to do most of this yourself, instead of waiting for him to do it.

In your shoes, I would clear the blockage in the bathroom, myself. There are several threads on this forum here. https://forums.moneysavingexpert.com/discussion/comment/52415145#Comment_52415145

Drain-snakes, plungers, boiling water, soda crystals, Mr Muscle type stuff, dismantling the U-bend, etc. Keep on going until you find a solution that works. Yeah, it's mucky and smelly! Or as a last resort, get a local handyman / helpful neighbour to do it.

TV in several rooms? Have you tried an Internal aerial ? Cost £10 to £20 ish. Obviously you only get terrestrial channels, plus freeview if you have the box. My sister gets a good signal by dangling an internal aerial with a booster out of the window.

Holes in the walls ? Yes, take photos first. If they're not too big, put some filler in, smooth it off with a filling knife from a pound shop. No one with an ounce of sense will ask you to remove it when you leave. Don't see how they make the place freezing unless they go through to the outside.

Exposed wires ? Keep the kids away from it and phone the council tenancy officer (or whatever they are called in your area.) to assess whether there is a danger or not.

Is the oven unusable ? If so, that is definitely something for the LL to do, but if he won't, then tell the tenancy officer & ask if they can help. You are paying for a place with a working cooker.

And try to find a better place. !

alta

Firstly contact your local Environmental Health officer (local council). However, it is never right to withhold rent, who do you pay your rent to? Who now holds your deposit? Did you have a inventory when you moved into the property? Ring Citizens Advice, they are very helpful and can point you in the right direction.
But Environmental Health is the best one, they have the power to legally make the LL bring the property up to standard, especially the electrics, and the oven, the plumbing should be looked at as it could be a health hazard.
Although I agree with others that some things are DIY by the tenants, under no circumstances should they deal with anything more than changing light bulbs a couple of times, it they keep blowing then there could be a wiring problem.
Get down and see the EH officer.

mysterywoman10

I'm really sorry you are having all these problems.

I think all the advice given so far is worth taking, the only thing I can add is not sure why you need a static aerial? Unless you are in an area with exceptionally poor TV reception? I only have one fixed TV aerial point in the house. Upstairs in the bedroom and elsewhere I have a portable aerials which work fine with digital I don't think any of them cost me more than £20 and if you move it goes with you! So not really sure why you would need to pay for Sky just to get a TV reception?!