I'm a final year PhD student trying to navigate the post-PhD life terrain.
i've been advised that it's best to find a post-doc with a team that has already got a project underway and has funding as opposed to trying to get my own funding and start my own project.
The issue i'm having, and I think it's common is that HOW DO YOU FIND THESE POST DOCS? I've also been advised that they're not usually advertised. So i'm assuming you have to get in touch with PIs.

I do have some contacts, however there are some people that I would love to work with yet I've never spoken to them and they probably don't know who I am. So how OK is it to cold email them? Is it seen as cheeky to ask if they've got any positions on their projects?

Any advice would be great! Thanks :)

One way could be through your supervisors. Also I think meeting and getting chatting at conferences can be a good way to get to know people, and then that way it wouldn't be out of the blue if you were interested in their work and wanted to do a postdoc with them. There are also mailing lists that sometimes advertise postdocs less formally. I'd be interested to hear what others suggest too.

Many universities have announced / will announce next week hiring freezes unless 'business critical' as the pandemic is leaving many institutions in real financial danger from what I'm hearing from my own institution and friends elsewhere. Unfortunately postdocs are unlikely to ever be seen as business critical. If you can, it might be better to hold off for a bit, and see if the government is going to bail out universities (see BBC and Guardian reports on this today) and then things may loosen up a bit. I'd also be looking at industry options very seriously.

I would be very surprised indeed if we emerge from this situation without seeing several universities disappear.
I would however say that many PIs will have secured external funding and I would suggest you continue to contact those who are advertising at the moment. There's a small window to get into a position and if you manage it you might be OK for 2-3 years. That might be enough to ride out the storm.
Unfortunately, not many businesses are going to be hiring either. Well over 1 million people have signed on for Universal Credit in the last 2-3 weeks and that's going to get worse.

As for cold calling, I have to say that my old supervisor always told me that if he had funding he would have either advertised the position immediately or would have allocated it to someone. He might not work the same as others.

In short, I would agree with TQ and Bewildered but with the exception that if I were you, I certainly wouldn't hold off until it was clear that window I was talking about had closed.

I logged on this morning especially to add that I definitely wouldn't hold off because of the current crisis (and then I saw pm133's reply). You might not get anything, but you might, so why wait and see.

Also, all of this depends on your field. I am seeing so many epidemiology related roles lately, medical statistics, etc.

What I meant by holding off, is that personally I wouldn't waste good contacts by speculatively emailing at a point, when the PIs don't know what's going to happen, when in a month things might be a bit clearer regarding funding (will new projects be delayed, or extensions given), the REF, when universities might be able to reopen etc. Applying for an actual job is rather different and of course you should do that.