Thanks Smudger. As you are also from the UK, we have a few common factors in travel plans. In fact, I have brought back KLM into reckoning into my own flight plans to Bali next September and having used them in June this year for the same destination, there are a few points to discuss.
First of all, I used Emirates once to go to Manila and regretted it; since then I have never used the airline for any Far eastern destination despite good connections from the UK. The reason is that the transit through Dubai always comes at an awkward time and it is so busy and tiring getting through the long security queues there that I was exhausted by the time I arrived in Manila. Since then I used Malaysia Airlines twice to get to Phuket and Sipadan respectively and it went well. MA also have a 30Kg checked baggage allowance and their fares are certainly competitive to Emirates. But the best part is the transit; what I did was to take the overnight flight (MH 1) out of Heathrow to KL, but booking the luggage through to the destination. The flight arrived in KL the following evening, whereupon I stayed on the airside with hand luggage and spent overnight in the Transit Hotel getting over jet lag. Thus, I was fresh and ready to catch the short flight to the destination the following morning. On the return journey I took the afternoon flight to KL and connected to the overnight London flight the same evening (MH 3). This plan worked very well.
The same thing can be done with Singapore Airlines except that until earlier this year they allowed only 20kg check-in for economy; now it is 30Kg and so they can compete with MA but SA tend to be more expensive. As things stand, they are some £150 more expensive for my trip but that might change.
KLM have certain advantages too despite a slightly more awkward flightplan. First off, they allow an additional 15 kilos for scuba gear (you have to pre-register this at the time of ticket purchase) over the normal 23 kilos for economy passengers; this is useful if you think that even 30Kg is not sufficient for personal luggage + scuba gear. Second, depending on where you live in the UK, you can get to Amsterdam from a more regional airport than the Heathrow. There is a daily direct KLM flight from Amsterdam to Denpasar, Bali (bypasses Jakarta but stops for I hour Transit in Singapore. You get off with hand luggage but simply turn around in the Transit area and get back to the same plane and same seat; no sweat) and you can book luggage direct from your UK airport (I used Bristol) to Bali. The only slight drawback is that the flight lands in Denpasar at 19:15 hours; Rather than take the long drive to Tulamben or Padangbai after a tiring long flight, one can spend the night at the cheap and cheerful Bali Ra Hotel next to the airport and take the transport the following morning.
I am not sure what your plan is next September but in Bali itself be sure to spend a few days in Padang Bai, an ideal base to be diving in both Candidasa and Nusa Penida to see Ocean Sunfish among other things. That is what I plan to do. If you have more time, go to Tulamben as well (Padangbai Dive resorts take you there). For Komodo, a liveaboard would be great and I used Mermaid 1 last June; Mermaids Liveaboards have the big advantage over all other Komodo bound liveaboards in that they depart from Benoa harbour in Bali, thus avoiding the hassle of an additional local flight. It was arguably the best of my 18 liveaboard trips to date.