Can MPs actually help with housing?

[MsHopey]

I live in a small one bedroom council flat. DH, 11month old DS and myself. We have severe mould and a leaky roof that drips into the living room in the rain or snow. We've informed the council who have put us on a very long waiting list to get it fixed.
I want to apply for a new property but can't go on the list till I've been here 2 years (we've been here 1 year and 8 months now)!
I've complained a few times about wanting to move and got no where because of their "blanket policy" on having to be in the same property for 2 years.
We started complaints pretty much as soon as DS was born as the mould has been affecting him.
Now, we're quite close with our downstairs neighbours. She has an 8 week old DD and has moved into her flat several months after us.
She's just came and shown us the council house she has been offered because of her mould problem, which she openly admits is no where near as severe as ours.
I kind of made my peace with having to stay here. But I feel like it's a smack in the face to move her family but not mine. So much for the blanket policy! I've emailed the council and my local MP explaining the roof and mould need fixing and/or we need to be put on the housing list (we live in the West Midlands so not a massive waiting list). Can MPs actually help?

Note: i do realise some people are homeless or struggling in life. I know things could be worse. I'm just wondering.
Also, DH works full time but on a shit wage so we can't afford private rent. We had to move into here from a privately rented house to budget as we were struggling.

MPs can't 'make' something happen. They don't actually have any statutory power. But they can make representations on your behalf and take up your case with the relevant council/government department. A letter from your MP to the head of housing, for example, will get more attention than one from you because of their position. Try and get along to one of their surgeries with some photos if the email doesn't work - an email might be read by a secretary whereas if you meet with them you can put it across face to face.

They can't get you a property and if policy has been applied properly then can't change the outcome.

But there will be timescales for replies. Who have you spoken to? Have you spoken to those above the housing/allocation officers? Followed the complaints procedure. If you can get it resolved without the MP it is best to do so.

Yes, they can one of my sons lived in a in a flat,[private rent] similiar condition to yours, i rang our MP and a councillor, and explained the situation, [should have said they had to move in with me as it was so bad, clothes and shoes going green mouldy]and they had a new baby,
Didnt even come to see us,Keys to a lovely 3 bed houes pushed through my door 2 days later
I have to say this was a lot of years ago though
Have you had environmental health round to see your flat,if not please do

I would imagine environmental health would be more beneficial.

I have had them out before to a privaite rented flat for damp and mould.

They got me out my lease early and fined the landlord if I remember rightly. Was a long time ago now though. So memories not 100%

But I do remember they where super useful and where really good to get on side.

I caught pnemonia from it and I remember a drs note having some weight as well about health issues etc.

This was more to a landlord being a dick about me getting out of a contract. But I am sure both those things would swing things with the council.