The BA fares should be available direct with BA but because there are so many options (connecting through KL, Singapore or HK but you can't specify which) BA's multi-city tool won't necessarily find them.

The PER-KUL-BOM is with Air Asia X - a long haul, low cost carrier based in Malaysia/Indonesia.

If you let me know the preferred class/routing I can post a full list of flight numbers and times.

It's also occurred to me that LUX-KUL|BOM-LHR can be done as a double open jaw for £738 in premium economy with Expedia. BOM-LHR is booking into E on a LUX point of sale, however, so you need to book via a UK TA to get that price.

KUL-PER is then £50 (!) - probably plus boarding and food - or £171 with a flat bed! You'd need to book in a fairly long layover, with flights departing KUL just after midnight or at 10 a.m. the next morning.