I would recommend trying to get a side job or freelance gig in addition to your main job. The advantage of that is that it feels like “free money” as all of that money (besides taxes of course) can go towards your savings in an interest-bearing account or ISA.
In software projects it’s easy to get ~5k/month gigs and most can be done remotely & part time, so it’s quite a nice bit of extra cash.
Credit cards & history
For credit cards I suggest having one and using it regularly every month up to 50% of its limit more or less, then paying it off in full after the statement was generated (you have to let the legacy rust notice your usage, otherwise they’ll keep reporting your balance as 0 to CRAs).
Get a copy of your credit report from the 3 main CRAs (you’re entitled to one free report per year as per the law), see if anything looks out of place. You can also sign up for free credit monitoring services such as Noddle but be careful to read their privacy policy, as a lot of them make their profits on shilling predatory scams (payday loans, etc) especially if you have bad credit. Consider signing up with a burner email address & phone to avoid their spam.
Close any old accounts that include credit & overdraft if you don’t need them, as lenders might deny you of further credit if they see that you already have “enough” (even if you completely forgot about those accounts and don’t use them).
If you aren’t already, get on the electoral roll; it’s a small signal but helps reassure lenders your address is valid. You can sign up online - make sure you don’t agree to be on the “open” (publicly available) register unless you like spam & scams.
Finally, don’t worry too much about it, credit reports are a dark science and while I see some people religiously taking care of it, I am not sure they end up in a better position compared to someone that doesn’t even think about it (but always pays the bills on time). At the end of the day the main objective of credit reports is to weed out bad payers - as long as you’re not one of them you should be good to go. I am not convinced that worrying about an account not being on all 3 CRAs or about account lifetime is justified, especially for mortgages where there’s a lot of manual review (as opposed to “computer says no”).
Things not to do
Lookup my Monzo account on the customer service tool and use it as an example of what not to do. 
As a start I’d recommend not saying “It’s Monzo time!” every time you get paid and going to the pub or shopping to spend it all.
Finally I’d say, do you actually want a house, and why? I see it as a huge liability - I very much value my freedom of moving around any time I want and not having to worry about selling it, etc. If you’re just falling for the “renting is throwing money away” BS, I suggest you read this.