That's what I ended up going for. I recall Shimano gears as something to aspire to having from when I was a teenager. In the end, I just bought a 6 speed 14-28T Shimano freewheel and compatible chain when I spotted an ebay seller selling both together.
just a point don't think that washer should be between the drop out and the mech hanger
It wouldn't shift onto the smallest cog if the washer wasn't there; the mechanism is at the limit of its adjustment. I may have to add another washer when I swap the 5 speed freewheel for a 6 speed, assuming there's enough adjustment left at the "other end" (sorry I don't know the correct terms, but hope you know what I mean).
If the gear shift mechanism doesn't have enough range to handle a 6 speed freewheel, I'll take it back to BikeStation where I bought it for £1 and swap it over for another one.