Oh, ok, that makes more sense. We did a lot of research into this a few years ago before our move - we eventually decided to head north of London to be near family. We were looking for a different type of property to you so I'm not so sure about budgets but in your position, I would concentrate on where has good rail connections into London plus easy access to the M1 or rail links to Leicester. Prioritise the journey you're likely to make most frequently
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We found there was a tipping point where house prices went down but the commute cost/time increased quite a lot. What you're looking for is that sweet spot where all three are acceptable to you
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I would look at places like Leighton Buzzard, which is quite near the M1, train into Euston, Milton Keynes nearby for amenities. You would probably get more house for your money in Bedford or Northamptonshire, but we liked Leighton Buzzard - it's pretty and quite green, with a nice feel to it.
The north/west side of Hertfordshire might also be an option - Hitchin is lovely, as is St Albans, but I suspect both will be out of your budget. We found Tring and Berkhamsted too pricey for us. Hemel Hempstead might be an option (or surroundings, eg Apsley). I have heard bad things about Luton but have to say, I don't know it personally.
For what you're looking for, I would probably stick to Hertfordshire, the west side of Essex near the M11, Bedfordshire and maybe Northamptonshire.