The 6 Series is built for this -long-distance cruising in luxury. The F06/F12/F13 640d with the B57 is the perfect GT: 45+ mpg, 600-mile range, and wafting comfort. The 640i with N55 is the petrol alternative; the V8s are for the emotionally committed.
The 6 Series is a grand tourer, not a commuter car -it's long, wide, and thirsty (especially the V8s). The G32 Gran Turismo is the most practical, but the 5 Series does the commuting job better. Buy a 640d if you must, but the 5 Series is the sensible choice.
The most dangerous badge on this site for a tight budget. A £6,000 E63 650i is not a cheap 6 Series -it's an expensive one with the first year's bills prepaid by nobody. A £15,000 F06 640d is the bargain; a £8,000 650i without a warranty is the trap.
The M6 with the S63 V8 is the full-fat experience -560–600 bhp, 3.9s to 60, and a V8 roar that justifies the bills. The F13 M6 is the one to buy; the E63 M6 with the S85 V10 is a masterpiece but carries rod bearing risk. Buy the best warranty you can find.
The E63/E64 630i with the N52 is a rising classic -the last naturally-aspirated straight-six in a 6 Series. The F13 M6 with the S63 is a future classic. Both are worth proper engine investment; the N52 is the keeper, the M6 is the investment.