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I have been trawling flight booking sites (expedia, skyscanner) for flights from UK mainland to USA in March/April next year. After many hours it is apparent that the less you pay, the longer the journey time and more connections you make. This seems crazy as you seem to end up doing MORE flying for LESS money. I am aware that there are subsidies and inter-airline and airport deals having arcane affects. Anyway, the best compromise between flying hours, number of connections and price is a journey starting in Glasgow, changing at Heathrow and terminating at Denver. I would prefer to travel directly from heathrow and cut out the other flight from Glasgow, but looking at the same return flight just from Heathrow to Denver DOUBLES the cost. Hence my question, if I book Glasgow to Heathrow to Denver, can I miss the Glasgow flight and turn up at Heathrow, check my luggage and catch the single flight to Denver and coming home, will I be able to get off at Heathrow and claim my bags without them transferring to the other flight to Glasgow?

No. If you miss any segment of the itinerary, the airline will generally cancel the rest of your ticket. If you don't show up for the Glasgow to Heathrow flight, they will not allow you to board in Heathrow (at least not without paying the difference in fare at the last-minute rate, which could be extremely expensive). Nor will they generally short-check bags for you.

Some airlines may make exceptions in cases where severe weather or other factors outside of your control have interrupted your journey, but they will not do so simply because the ticket is cheaper; that is precisely why they charge different prices depending on the cities involved.