HSBC (and I imagine most big banks) credit cash paid in at post offices immediately and cheques only take one extra day compared to going to a bank branch (and that’s if you can’t pay in cheques via their app)
If I was you, I would get an account with someone like Starling, Lloyds/Halifax or HSBC instead of the two banks you are considering.
there the only 2 i can get
Then it seems that you should opt for one or other of those two banks. If they will give you an account without ID then that’s the most important point. It doesn’t really matter what anyone here thinks.
I wish you good luck. 
Why?
If it’s due to lack of ID, the banks will have policies which mean other things can be accepted instead of a Passport/Driving Licence.
yh but when ive asked its proof of address which i got but i dont have id
Just using HSBC as the example but if you look at their list of acceptable ID it includes
Her Majesty’s Revenue & Customs (HMRC) tax notification
HMRC will send you on request if you need one.
Other big banks will also accept a HMRC letter as proof (Lloyds as another example).
In fact, HMRC documents can usually be used as either proof of ID or proof of address depending on what someone needs.
i dont get any letters from them
You can request a letter from them with your tax code on it, I think.
You just phone them up and ask for it.
For now though, you probably should just stick with either/or Co-op or TSB. If clearing times at the Post Office are important to you, go with the fastest one?
TSB are a bigger bank than the Co-op, so have more branches if that is important.
Both have pretty simple apps, but TSB’s is probably slightly better.
Both are likely to be sold and eventually merge with other banks in the medium to long term.
I just moved from coop. I only use online services for banking and in seven years only visited the branch to open the account. The app is rubbish. The other fact they’re are about to be taken over by some hedge fund and that made the decision easy.
They are already owned by some hedge fund, I believe.
Coop sold out three years ago @Darren2455
I bank with TSB and moved over a year ago from full monzo. I haven’t had any issues with TSB so far and they have been making major improvements to their banking app.
Yeah I did mean to say some other hedge-fund😊
I mean you came to a Monzo forum to ask about 2 legacy banks. Not sure what you’re expecting.
One of my relative is with Coop bank and never seems to have any issues but they’re quite private about that sort of thing. We send each other bank transfers often and is quick, about all I can say.
After what happened after the TSB migration in 2018 I wouldn’t touch them with a bargepole but that’s my two-pence.
A bit of a kicking, then some measured advice by the looks of it. 
I’m with Smile bank (which is a online only part of the Co-operative bank) and use it as my main account. The mobile app is nothing fancy but works well enough.
Believe it or not in the late 90’s when it was launched Smile bank was state of the art but is now definitely showing it’s age, mostly due to lack of investment caused by the madness going on back then with it’s parent company.
I would if I were you consider that if you don’t care about branch banking* Smile isn’t a bad choice.
*Pay in and send cheques via the post office.
Of course that’s all dependent on if the KYC requirements are the same and they ask for the same ID.
I just left TSB and they were awful and stuck i the 20th century. To change my address, they made me go into branch, and had many other customer service related issues
Of legacy banks (I’ve had accounts with most of them at some point), HSBC are generally good and helpful, and most things can be done from internet banking
I’ve been with Smile since they started. As mentioned in a previous post, they were state of the art when first opened but have stagnated in the last few years (a bit like Monzo appear to be doing now).
Nothing bad to say about them. Good, solid, bank as long as you’re happy with behind the bleeding edge. Mobile app and website are functional (if dull). They always answer queries in a timely fashion and there’s a call-center to fall back on.
I would say their customer service was good, others may disagree. Much better than the other high-street banks, certainly.
Smile customers can use Co-op bank branches without any problem. I’ve been doing that since Smile opened. We still have a joint account with them because it offers an overdraft - plus can pay cheques in at the branch.
Their app and website are both awful, but they’re reliable.
Great point but since the Co-op Bank has closed so many branches to save money it doesn’t make sense, especially where I am in London.
There is a branch at Wood Green which doesn’t make any sense as it’s too far away then there is one at Ealing same story and oh there is one in Watford…Doesn’t make sense.
So the Post Office it is then. Of course if your blessed to have a branch nearby then you have the best of both worlds but others are not so lucky.
I did once have two close to me but guess what both were closed. Never used them as I didn’t need to.
Not true IMHO it’s fine, I’ve never had a problem with it. Apart from the week that they were down*
but that affected everyone. *Smile and the Co-Op customers.