Through customs at Heathrow (T3), and get back out again?
 

As I have an 11hr wait at Heathrow coming up (landing in T3,leaving from T5, different tickets/airlines),and I am thinking about buying an extra ticket with Virgin Atlantic just to be able to pay to get access to their lounge. I understand that the Clubhouse lounge is airside? Will I be able to get out again, collect my baggage from a deposit box and go to T5 to take my BA flight?

And...will it be worth it? About 120 GP? I am considering some of the other lounges as well

Book them under the same ticket using a travel agent. That way, you don't have to pay the taxes. You can enter the UK as you please if you have the right documents, as long as you have enough time to make it through security for your onward flight.

I've done this in NRT before to eat some sushi air side.

Some explaining.
 

I have already bought the tickets, and understand that I can go to London between my flights. But: can I enter a lounge and go through customs, and then get back out again without flying?

I re-read your question and I assumed the lounge was land-side. I can't answer about being able to exit terminal 3 for a second time. However, isn't there a land-side shuttle connecting T3 and T5?

You can also check if the carriers have interlining agreements. That way, you won't have to claim your luggage at all in LHR. I suggest you keep things simple and just buy a pass to the BA lounges, if they permit.

There is airside access between the terminals with the FCC (Flight Connection Centre) -- I think that is what you meant. One could also go between the two terminals landside as well, there is a HEX link into T5.

I agree with you, best to keep things simple and to access a lounge in the terminal the OP is departing from. I would also suggest the OP has checked luggage interlined so that it doesn't have to be claimed at LHR (assuming an interline agreement is in place between the first carrier and BA).

It's been a couple years since I've been to LHR - I purposely avoid it - but I believe British Law requires inbound and outbound passengers to be separated. Some of the terminals at LHR aren't the best designed for this, but I know they've been making upgrades at LHR (and even LGW) to stay in compliance with this law.

Upon arrival I believe the OP would either have to proceed directly to the FCC (Flight Connection Centre) or proceed landside via Immigrations/HM Customs.

To me, it sounds like a lot of hassle just to access the VS lounge. If it were me, I would either hop on the HEX and go into the city and/or get a day room at a hotel near the airport. If the OP wants a lounge on departure, I would suggest looking into obtaining access at a BA lounge.