How do police download phone data

My phone has been siezed by the police to try and prove I sent some emails from a Gmail account. I have deleted the app from that phone and deleted that Gmail account. Can the police recover this?
I also had a photo on there which I deleted. Can they recover this?

If you've provided them with the means to unlock the phone, then recovering that data will be trivial either from the storage or from backups. Even without this, with the right info from your ISP they will almost certainly be able to associate your phone with those messages being sent.

Yes bit that Google account has been deleted so how would that affect it?
Also what about that photo? I've been told they are not necessarily looking for that photo but how likely are they to recover deleted photos i.e. how can they find it if they don't know what there looking for?
Is it true the police/cps are understaffed and prioritise putting resources into more serious cases?

Anything that was stored locally on your phone is almost certainly still recoverable, they will find the data associated with the data contained in the emails they're trying to find the source of. And even if you delete the account, the data of everything it sent and received will probably sit on Google's server in perpetuity, precisely for moments like this where they might have to comply with requests from law enforcement.
They don't need to know what they're looking for if they simply look at everything.
I can't speak for the state of funding for the digital forensics team of whatever department has your phone, however my guess is if didn't have the resources or intention of searching your phone, they wouldn't have bothered confiscating it in the first place.

What do you mean locally?

Stored directly on the phone itself, not online/cloud storage.
In all honesty I think you will struggle to find someone on a student forum who is familiar with the inner workings of police data recovery techniques.

What do you mean locally?

There's nothing I can do now....my life is in the hands of someone and if they decide to give a statement then I've had it. I've lost it all....my job my clean record.
I keep telling myself the allegation isn't too serious hence why the main complaint hasn't even given a statement

Sounds like you should speak to a solicitor and follow their advice, I'd you haven't already.

I have I'm on police bail being investigated hence why the police have taken my phone.
At my interview I made it clelar to my solicitor i'm happy to plead guilty if it means I don't have to go through this every day with this hanging over my head but there was a lack of evidence.
Also what tactics can the police use to get a statement out of someone? Surely they can't manipulate or vrive or coerce someone?

Well I've been told that there not looking for that all there trying to prove Is that I sent them emails. When I was arrested they only took my phone not any other devices

There's nothing I can do now....my life is in the hands of someone and if they decide to give a statement then I've had it. I've lost it all....my job my clean record.
I keep telling myself the allegation isn't too serious hence why the main complaint hasn't even given a statement

The police can still investigate an alleged offence without a formal complaint, same as a prosecution can go ahead without the victim's if it meets a two-stage test: is there enough evidence against the defendant (a realistic prospect of conviction) and is it in the public interest for the CPS to bring the case to court?
It happened with the high-profile assault case against Caroline Flack, where it went ahead without the allegation being supported of her boyfriend.

That's true bit this isn't a rape case or a domestic abuse case where the victim is too scared or embarrassed. If my complainant really wanted to take action she would have but she didn't even when the police approached her.
All the evidence they have is a bunch of emails 2 statements from the university staff and my phone (there's no guarantee they will find anything). So this can't become a victimless prosecution as they have nothing from the victom.

So they've got evidence against you, and if this stalking and harassment why wouldn't the victim be feeling scared and not want to make a statement?