Can rent from a UK property be moved into an investment account if the owner lives abroad?

I'd like to rent out (let) the house while I'm living abroad and I'd like that rent money to go into a managed investment account. Is this possible in the UK or would I be prevented from re-investing rent money because I'm living away?

It's completely, totally, possible and normal. 10,000s of brits do this. It is not illegal or prevented in any way.

It's completely OK whether you do or don't have a mortgage.

(If you're asking about tax implications, you'd have to ask very specific questions.)

What you do with proceeds from a rental property are entirely up to you.

As long as you pay any taxes due (and there are special rules for landlords who let property in the UK but live abroad), and have a contingency fund available to pay for any issues that come up (e.g. repairs, bills when there are no tenants, decorating, refurbishment, etc), then whatever is left over is your money, to do with as you please.

From a comment:

Is there a certain type of property agent/solicitor/other that I should look to contact for this sort of thing?

I don't know for certain, but lettings agents typically ask for a bank account to pay rent into. It might be possible to nominate an ISA - however, you might just want it to be paid into a normal bank account, so you can keep hold of some of the cash for contingencies. You can then manually move the rest into an ISA. (I'm assuming you'll do all of this online.)

Should I expect to make almost no money at all from the rent or is it actually worth it?

Being a landlord can certainly be a profitable business, so long as you do your homework. There is considerable resource online and elsewhere on the matter.

Note that if you're renting out your own home, and so have a residential mortgage, you will either need permission from your current lender before letting out the property, or you will need to replace the mortgage with a buy-to-let (BTL) mortgage.