Re: I'm gonna borrow a friend's story here. I wish this wasn't true.
Yes, in the UK, PME (Protective Multiple Earthing, TN-S or TN-C-S - see e.g. https://www.lsp-international.com/power-supply-system/ for an explanation) is the norm - though there are still places that use TT and their own earthing rod. When PME was being rolled out, typically the user's own earth rod would be disconnected - but with the latest revisions to the wiring regs, we were expecting specific advice (requirement) to install a local earth rod as well as the DNO's (Distribution Network Operator) earth.
The benefit of PME is that the DNO provides multiple distributed earth points, resulting in (typically) a much better earth than any single earth rod (spike) would do. This means a low Ze (fault impedance of the supply to earth) and reliable tripping of over-current protection in the event of a fault. For TT supplies, the earth rod is typically not enough for this and some form of earth fault detection is required - historically this used to be a VOELCB (voltage operated earth leakage circuit breaker) which actually tripped on current in the wire to the earth rod, but since they would not detect a fault to a different earth (e.g. via a water pipe) these days it will be an RCD (residual current device, detects a difference in current between the live and neutral conductors).
Now, to the question of what happens when there's a lightning strike. The important thing to remember is that these are very high currents, mind bogglingly high, and with incredibly high rise times (i.e. the current increases very very rapidly, before decaying almost as rapidly) - thousands of thousands of amps (i.e. mega amps) for milliseconds is roughly the order of magnitude. The second thing to remember is that "ground" isn't some mystical material with infinite conductivity - in fact, it typically had a fairly high resistance. So those that know even the most basic facts about electricity will realise that a massively high current passing through a significant resistance will create a significant voltage drop. So when a bolt hits the ground, immediately around it the "ground" may take up a voltage gradient measured in hundred of volt per meter distance close to the strike, and rapidly reducing with distance as the current is distributed though a greater mass of earth.
I've dealt with the aftermath of this. Years ago (when serial lines to terminals was the norm), we had a client in a rural location. From the description, I think they had a lightning strike to ground a field or two away - I'd guess perhaps 200m or so. This was quickly followed by a burning smell from the room that housed their server.
While everything shared the same electrical earth from the DNO, the combination of potential gradient in the ground, multiple connections between electrical supply earth and the building frame, and so on meant that there was significant voltage gradient between different pieces of equipment. Luckily, most of the old Wyse 60 terminals just lost their RS232 converter chips which failed (fuse like) and protected the rest of the circuits. But those in the second building, with separate electrical earth, and further from the strike, had much more damage. But the poor old server took surges from multiple connected devices which fried it's serial cards (and I think, the motherboard).
And that is why, it is good practice to use fibre for any longer runs (even within the same building), and especially between different buildings.
As to connecting the LPS (lightning protection system) earth to supply earth, that's not as clear cut as it might seem. Guidance in the wiring regs (BS 7671 in the UK) is that they should be connected - and you should have surge protection in the power supply system. The idea there is that should there be a strike, the LPS will conduct it to ground and there may be a difference between that ground and the supply ground - meaning that there's a risk of flashover to other services. If you connect them, then the whole system changes voltage at the same time, with the surge protection keeping live, neutral, and earth at reasonably similar potentials, and this avoid the risk of flashover. That does require a reasonable earth electrode for the LPS, which reminds me that it's something I still need to address at our church ...