In the calibres that you are looking at, a 30-06 and 9.3x62 falls within Rigby's 'Highland Stalker' range, at a base price of £9,180, and the .375 falls within its 'Big Game' range which starts at £9,120.
The equivalent Mauser models start from £9,100 (for the smaller calibres) and £12,800 for the .375.
These are, of course, the base prices, and the firms concerned will try to sell you various upgrades which can easily see the price increase rapidly. Nonetheless, given that a Mauser rifle with 'Rigby' engraved on the barrel and English proof marks will hold its value better than a Mauser rifles without these important aids, for the relatively small difference in price it would make sense to buy a new Rigby rather than the Mauser; it would certainly make sense in respect of the .375.
Bear in mind that as soon as you take possession of your new rifle and walk out of the shop, you will have lost about 40% of what you have just paid for it, and that out of taxed income.
If you keep your eyes open, and are prepared to put up with the onerous bureaucratic hurdles imposed by politicians to prevent us plebs taking pot shots at them, it might make sense to buy your rifle second-hand; ideally from an auction house - always get a condition report before you bid - or even a dealer. For example, although I live in the UK, my rifles typically have been bought at auction and from abroad: an H&H and a Jeffery came from Denmark (the H&H costing 2/3ds and the Jeffery 1/6th of the new prices, quoted above), and a Rigby came from Germany. And that way you can buy two rifles instead of one!
By the way, a bit of matrimonial advice: buy a piece of jewellery for the wife at the same time as your rifle. It neatly undercuts any arguments about (1) only spending money on yourself; and, (2) spending money on something you will never use.