I have spent some time searching for the most economical and straightforward method of getting from Manchester to Heathrow in July. I can't seem to find anything that isn't either expensive or complicated. To go from Manchester to Adelaide proved difficult hence the departure from London.
Train to London then tube to Heathrow is cheap and simple enough - provided you get the right advance purchase tickets. It will be April at the earliest before these become available for July.
Alternatively train to Reading and bus to Heathrow. Ditto about cheap fares.