JohnnyUMF:

There are a significant number of charter flights each week from London Gatwick to Tel Aviv with the UK charter airlines - Monarch in particular has made a specialism of these for years, and others operate as well. I can't recommend one particular such operator (others probably can) but surfing the web with Gatwick and Tel Aviv (there are no scheduled flights between the two) should bring results.

It is precisely because the regular fares are high that such charters continue, in the style of transatlantic ones in the 1970s.

In the winter when there are less flights to Tel Aviv there are also charters from the UK into Eilat in southern Israel which you could consider. A problem of course is you are wanting the very peak week for demand, and many of the seats will have already gone.