Travelling from Istanbul to Moscow overland is adventurous at best. For example, there's a big country between the two places called the Ukraine.
Assume you take the Asian route, you will almost certainly pass near Kharkiv border and other hot spots along the border of eastern Ukraine. These would include Donetsk and Lugansk. Anywhere near those places exposes you to robbery, kidnapping, and possible loss of life.
Along the way, you would pass through Georgia. You'll need to avoid the volatile regions of South Ossetia and Abkhazia, If your passport has stamps from these or other separatist entities you will be in trouble with the Russians when you get there. Note that if you enter or leave from Dagestan, Chechnya, Ingushetia, or North Ossetia, you may be detained as an illegal entrant.
Georgia will honour a UK driving permit, but driving at night is risky verging on outright dangerous. Wandering livestock, for example, are not clearly visible due to the poor lighting. If they notice you're a foreigner, you're fair game anyway. So if you're driving at night, do not stop for any reason, and be sure you have enough petrol to carry you through the entire night.
Travelling by train through Georgia is only slightly less risky. Keep the door locked, and of course never leave your stuff unattended.
After transiting Georgia, you will be in the Caucus, most likely travelling through Stavropol. Stavropol City is safe enough but the Stavropol Krai is a tinderbox of hot spots. Avoid Budyonnovsky, Levokumsky, Neftekumsky, Stepnovsky whilst transiting Stavropol Krai, and if you get in to trouble, don't expect immediate help from the Consulate.
From Stavropol, it's almost impossible to head north without getting near the border of East Ukraine. You can take a difficult overland route to Volgograd and travel in safety from there onward, but like I said, it's difficult. Travelling from Stavropol to Volgograd takes about 4 days through desolate poverty. No fun at all.
If you take the European route from Istanbul to Moscow, you'll be generally safer. Moldova and the West Ukraine are mostly stable and once you hit Belarus it's safe. As long as you define ANYTHING safe in that region. Overall, the European route is safe enough to consider a trip, but it will take a lot longer than the Asian route. So it's really your call. Like Clint Eastwood said, "Do you feel lucky?"
Finally, it's always sound advice to read this: https://www.gov.uk/how-to-deal-with-a-crisis-overseas