Manchester-London-Tel Aviv. Chance of cancellation of first leg? Safe to check bags through?

The only way for you to retrieve your bags in LHR is to book the two flights separately and "self-connect".

With a regular connection, this is what happens in LHR:

• You go from your arrival gate to your destination gate
• Your luggage goes from your incoming flight to your departing flight.

(*) Note that flights to TLV may have specific procedures I'm not aware of, but this is the general procedure.

If you self-connect, then you need to:

• Deplane and go to baggage claim
• Wait from your luggage (yawn).
• Exit the secure area
• Go to the departures area
• Find the check-in area for your flight
• Queue (re-yawn)
• Check-in before the check-in deadline (that should be 45 or 60 minutes before departure depending on whether the flight is short-haul or long-haul)
• Go through security (triple yawn)
• Go to your gate

Your luggage would have to:

• Go from your incoming flight to baggage claim
• Go from the check-in desk to your outgoing flight

Notice how many more steps? That increases the risk of something going awry tremendously, not to mention the fact it takes a lot more time.

Also, if anything wrong happens (first flight is cancelled or delayed, luggage is delayed, there's a huge queue at check-in or security in LHR...), then:

• If both flights are on the same ticket and your luggage is through-checked, they have to take care of you. It may be suboptimal, but they will try, and they have lots of obligations to take care of you (rebook you on the next available flight, pay for hotels if you're stranded overnight...), and you may even be owed compensation.
• If you self-connect, you're on your own. If you miss the second flight, you'll be considered a "no-show". Your ticket will most likely be cancelled outright (possibly including any further flights on the ticket such as the return flight), and you will have to book and pay for a new ticket at the last minute, at last minute prices. The fact that you were flying on BA does not matter a second if it was not on the same ticket.

Unless you spend the night in London (or a good chunk of a day), self-connecting is just a bad idea, especially these days.

Is it likely the MAN > LHR flight will be cancelled?

No one knows. LHR has announced that beginning July 11 (and ending September 11, 2022), fewer flights will be permitted, but it'll be up to individual airlines as to which flights will fly and which will not. What British Airways will actually do is up to British Airways. You can find more info on this British Airways page. Were I in your spot, I'd check regularly to see if BA has delayed or cancelled either of your flights. Bottom line: This is a matter of opinion.

It is likely — here's another opinion — that train travel will be less impacted than air travel. You might consider taking the train to Heathrow instead of flying.

Safer to retrieve bags at LHR than check them through to Tel Aviv?

Retrieving and redropping adds several handling steps for the airline's and the airport's baggage handlers. Each step increases the possibility of physical damage as well as misdirection or falling out of a truck or off a conveyor belt. Retrieving and redropping also adds to your duties (standing in lines, carrying luggage from one place to another, dealing with airline or airport staff) during the time you're at LHR, which will likely be crowded and uncomfortable. On the other hand, if BA cancels the flight to Tel Aviv at the last moment, you'd at least have your luggage with you.

Checked-through baggage is much easier for the passenger...if the flight goes as scheduled and the baggage doesn't go astray. While the vast majority of bags make it to their destinations correctly and on time, some don't.

Whether it's safer to check or carry depends upon your risk tolerance and your energy. What's the best for you may well be different from what's best for others.

Retrieving your baggage at Heathrow and rechecking it would be a very bad idea.

One of the main problems that Heathrow is having right now is not enough capacity to get passengers through security, hence very long queues. If you collect your baggage and re-check you will then need to go back through security. Depending on timing, you might not make it. (You're also adding to the problem for other people, of course.)

Even when things are running normally, it's always possible that a bag will get delayed or lost, even without a transfer. The usual advice is to make sure you have any essential medicine, anything you critically need for the trip, and ideally things like a toothbrush and a change of clothing to make the first day or two more pleasant if that happens.

With through checked baggage, if anything goes wrong it's BA's problem. If your baggage doesn't make it onto your second flight, BA will put it on the next flight to Tel Aviv. If you were to collect and recheck your luggage, then if anything goes wrong it will likely be your problem.