certainly one of the major package providers does 4 weeks, but can't remember which. I think maybe Thomson/First choice
Cheap and cheerful flights?
we've used Qatar ex manchester (if flying from the north that is virtually your only option), they are good flights but, unless they are having a sale etc, are not cheap.
we've paid approx £760 each for next January as an indication.
Unable to recommend any hotels as I have only experience of one booked independantley and would be reluctant to advice anyone else to stay there in case of dissapointment if it's not what you want. eg pool etc.
I too have heard of people booking flights over there, but can't see how two single flights will work out cheaper than a return, but could easily be wrong.
Someone with better advice re this will be along soon!

We go for about 2 months each year.
We book flights to Mumbai through Southall travel, then internal flights with Cleartrip.
If travelling from the south then you can get direct flights to Mumbai from Heahrow.
We travel from Birmingham and have 2 flights to Mumbai. (Paris, Munich, Dubai) then on to Mumbai.
We have travelled with Air France, Lufthansa and Emirates over the past 5 years.
Our experience is that the cost is slowly rising but booking about 2 months before leaving we tend to get reasonable costs.
Two years ago we paid £under £400 to Mumbai.
This year was £475 to Mumbai with Emirates our most expensive. The return trip from Mumbai to Goa works out about £65-£80 depending on exchange rates.
Most regional airports have airlines that will get you to Mumbai in 2 flights. This saves the time, effort and cost of travelling to Heathrow etc.
Accomodation, we now rent an apartment but have booked a hotel for 2 nights before then looked around at guesthouses during the first couple of days.

4 weeks flight only shouldn't be a problem whether chartered or scheduled.

The cheapest I can remember in recent years was £ 510 per person for direct flights out of Gatwick. Never paid more than £ 600.

As Sam said the best deals seem to be 2-3 months before travelling but I'm afraid its a matter of trawling the net for them - i don't think I've ever booked through the same company more than once.

We usually go mid to end of Feb but for 3 weeks max - many of our friends stay for much longer though.

Hotels is a bit of an open question, it really does depend on what you want & expect for your money - The best hotels (in no particular order) I would consider to be Taj; Santana; Highland Beach; Sunset Beach; The Fortune; Girasol; Phoenix Park; the posh one by Sunny Side Up (never can remember the name) but there are others. There are also many, many budget options that are basic but clean. I'd take a look at the hotel review section and work from there.