US to Italy with Layover in London

You are confusing customs and immigration.
Customs is the check on goods. What you have in your luggage, whether it is allowed into the country and whether and customs duties (taxes) have to be paid. Customs takes zero time as most people are not stopped.
The EU is a customs union. There is no customs between EU countries.
Immigration (aka Passport Control) is the check on people, whether they are allowed into the country and for how long. This is where they stamp your passport if necessary. Immigration can take 30-90 minutes depending on how busy they are.
The Schengen Area is a passport union. There are no (regular) passport checks between Schengen Area countries.

Is this one through booking, or two separate bookings?
If one booking, your bags will be sent directly to your final destination and you will stay "airside" and not go through UK immigration. the procedure is:
Land - disembark - possibly change terminals (airside) - security - board
You have enough time.

You have done this as two separate bookings. Which means you have to check in again for your second flight:
Land - disembark - go through immigration - luggage reclaim - customs - exit to arrival area - possibly change terminals - check-in (BA) - security - immigration (leave UK) - board
Time will be tight, and if your first flight is late you are not covered.

In both cases you go through immigration when you land in Italy.
You need to find out which terminals your two flights are using. Some Heathrow terminals require a train between them.

This journey requires a change from Terminal 3 to Terminal 5. Presuming you are not having to reclaim and check bags as covered above, do this airside by following the signed transfer route. You will then go through security in T5.

In what circumstance wouldn’t I need to reclaim my bag? The two airlines are different BA and Virgin. Would love to do this airside

In what circumstance wouldn’t I need to reclaim my bag?

Did you do this as one purchase, or two separate ones?
If it is one purchase, one ticket, then you can check in at your departure airport all the way to Italy, you will not see your bag at Heathrow, you will stay airside and it will be (relatively) easy. Just because it is two airlines does not prevent this happening, many airlines transfer bags between them.

If you have made two purchases, two separate tickets, you need to enter the UK, collect bags, transfer terminals "landside" (train) and check-in again in the public area. This will take a lot longer, and if your first flight is late you do not have any fallback.

This journey requires a change from Terminal 3 to Terminal 5. Presuming you are not having to reclaim and check bags as covered above, do this airside by following the signed transfer route. You will then go through security in T5.

Not necessarily, BA are still operating flights out of T3, my most recent one to Miami was T3 and so is my flight to Prague. Also flew to Warsaw from T3 with BA.

The Heathrow BA flights to Rome all presently are from T5. Not that this could not change in the future of course. The BA flights in T3 are tend to be the ones carrying fewer transfer passengers (and therefore often more holiday-orientated), although there are exceptions..

If you can do carry-on bag only (no checked bag), and you print your boarding pas for the second flight ahead of time so you have it in hand, you can do the airside transfer from T3 to T5. No immigration line, but you will go through another security check. This is so even if you stay within the same terminal.

Virgin Atlantic does NOT list BA as an airline partner. It seems unlikely any checked would be 'checked through' to Italy.

OP seems to be traveling with checked bags.

With checked bags everything would have to run with the precision of a fine Swiss watch to have a ghost of a chance to be successful. With carry on only the chances improve a bit.

If tickets are already purchased, I would be exploring the "plan B" options to get to Italy. Might want to explore the change fee cost for the BA ticket to change to a later flight, vs the walk up cost of some bargain rate carrier.

All in all, 2 hr 20 min may be enough time, but that is not how I would bet.

Virgin Atlantic does NOT list BA as an airline partner. It seems unlikely any checked would be 'checked through' to Italy.

BA has to interline bags with Virgin Atlantic (and some other carriers it is not in alliance with) as part of the agreement with the CMA that allowed it to buy British Midland.

Marco

Thank you for that illuminating fact.

Not something that seems to be readily apparent on the Virgin website

They probably don't want to advertise BA … but if you book a single itinerary, then the bags will be transferred. All bets off for two tickets of course.

Given that this is two separate bookings, I'd be hesitant to go with a two hour layover. There are many people who'd be fine with that, but as a poster child of Murphy's Law, I know to hedge my bets. I always allow for things to go wrong and give myself enough time. While navigating Heathrow is not that difficult, there is no guarantee that your first flight will arrive on time OR that the lines will be short enough for you to zip through them.

For that booking, I'd look at a four hour layover at minimum. That's just me, based on my own past experiences. Somebody else will laugh at that, but I don't have the money to lose if I miss a second, separate flight. In fact, I'd consider arriving in London - spend the night - fly out the next day. YMMV.

The OP hasn't definitively stated whether this is one or two separate tickets.

You're having a lot thrown at you and may be getting a little confused. If you could help us with some more specific information we may be able to help better.

1) Where are you going in Italy. It's a big country with lots of airports. British Airways flies out of both Terminal 5 and Terminal 3 at Heathrow and which terminal you leave from will help. (We don't know until we know where you are going.)

2) When you bought your ticket, did you buy it all at once meaning it is on the same itinerary with the same 6-letter record locator or two separate ones. (If you look at your e-ticket or ticket receipt there will a six letter code. There will either be one or two.)

3) Are you definitely taking checked bags?

If you go to Heathrow Flight Connections and fill in your two flights you will get step by step instructions on what you have to do. But there might be some modifications depending on your answers above.