Welcome to the forum Dave. The Peak District is a great place for mountain biking. In fact I was out yesterday and passed through Buxton as part of the loop and the popularity of the area was emphasised by the number of cyclists that were still out riding despite the cold and snow. Fantastic!
Of the bikes you have mentioned, having looked at the spec's I would say the BMC and Cube gives the best package, pretty closely matched except the BMC has better hubs. The White has components from lower down the pecking order but this is maybe reflected in the price as it is the cheapest with some compromises on the components (No name hubs & Tektro brakes!). I don't like the idea of 29" MTB wheels but have never ridden one so shouldn't really comment. I am still riding my mid 90s GT Zaskar and find it a fantastic ride on the old skool 26" wheels. My oldest son has an Avalanche with 27.5 wheels and I have only had a short ride on this but it still feels pretty nippy, just not quite as nippy as the Zaskar. If it were me faced with the choice of this 3, I would most likely go for the BMC.
What GT bike do you have? It might be that with a few minor upgrades you could improve your current bike without spending such a large amount of money.
So your job is basically buying a bike for you, as an incentive to commute by bike, but you may only do it once a week or so when you have a short shift (and the rest of it is 'messing about in the countryside'? This seems to me like taking advantage of them and trying to get a free new bike. It would be a helpful program for someone who truly wants to commute and has no bike, it would get them equipped.
Cycle to Work is not free bikes provided by an employer! The bike is purchased through salary sacrifice, so you pay back the purchase price in instalments that are deducted from your salary over a 12 month period. The benefit is that you receive tax relief on the bike deductions so you do save some money, around 20-30% of the full cost. This is a government backed scheme to incentivise cycling, reduce commuter congestion and improve health.
The downside of the scheme is that the bikes are usually only available at full list price, or even incur a handling fee from some suppliers. The bike purchaser can often match the savings of using the scheme by shopping around the discount sellers or buying the previous years model at the end of the season. For some, the scheme is effectively an interest free loan that allows them to buy a better bike than they could ever afford to pay for in a one-off lump sum.