Oh OP you are me a few years ago. Have to say though, if your Mr picky is looking like everyone else for Georgian splendour, within walking distance of a town centre, and a lake, in commuter belt, you really aren't going to get any change out of £3m. You won't find it either, as someone with £4m will beat you to it.
One question though, have you actually lived the period property dream before, or are you just imagining what it might be like? Because the reality is very different. I speak from experience, 6 years into the joy that is period house living. Do you read Fay Weldon? If not, start. She has a fabulous short story about how period houses lure you in with their looks, then drive you half mad, bleed you dry, and wreck your marriage, before spitting you out, ready for their next victim. Ours has done all of that, although DH and I are still married. Just!
So, here's my advice: original oak flooring is drafty and dusty, flag stones are freezing, insulation is non existent (you will be cold, most of the time), sash windows have a draft effect equivalent to a 6 inch hole in the middle and secondary glazing is about £700 for one large window, heating systems are likely to be archaic, and oil, drainage may well not be mains but a cess pit (avoid avoid avoid), you will get mice, and wasps, and in you are really lucky bees down the chimney (if you are us you will get them twice 
). You will need a handy man, on call, possibly daily for at least the first 2 years. Guttering will fail and rot your walls, bits of ceiling will fall in when you least expect it, usually when your DH is away on business, and if you don't have a friendly Mr Can Do, ready to come out at a moment's notice you are in trouble (mine is called Paul, and you can't have him ). Everything is different for a period house - you will need to learn this. Mortar is not mortar, it must be lime, or your bricks will spall. Spalling bricks are bad and cost money. New tiles must be reclaimed, and expensive. You will spend disproportionate amounts of time sourcing these as they drop off at a rate of seventy million, per year. Plaster will likely be shot, but under 6 layers of 1970s wall paper, so when you peel this back, the entire wall will crumble and and you will be left with a sorry looking layer of wattle. Local plasterers called John will rip you off. This is another reason why you need a friendly Mr Can Do, because he will have friends who can do more, and a recommendation is worth more than a yellow pages ad. Damp proofing is not apparent, nor are cavity walls, everything water related is different. Rooms are kept dry through air bricks, and ventilation. Cover these at your peril. Paint must be breathable, wall paper is a BAD idea, and whilst secondary glazing may keep you warm it will mould your walls. As heating is way too expensive, best option is 59 jumpers and an open window. If you do not have 59 jumpers, buy them, now, before you move. Finally though, don't forget. The very best thing about a period property, it will by definition be miles from where DH works, so you will never see him, and when you do he will be dressed like a tramp, whilst he dries to unblock the cess pit/patch the ceiling/locate the rats in the grounds, and in a stinking bad mood. He may well also be stinking. Cess pits do that.
And finally, check if your vendors a bit starry eyed and mad looking. Is the woman stick thin, and the man bald. Are they us? Are they moving to a new build???? Ask why 
Good luck OP, and my condolences.