British Airways together with Iberia are allowing to book some interesting open jaw flights to Kuala Lumpur/Singapore. You would have to look for flights departing from Barcelona or Madrid and returning back to London. The cheapest open jaw flights are currently starting at £259/€303! Some of the flights may require long layover in London on your outbound flight. This is some great option to make two separate trips at once and for such an attractive fare..
You may consider to book open jaw flights either to Kuala Lumpur or Singapore. Another and even slightly cheaper option would be double open jaw flights when flying from Europe to Singapore and returning back from Kuala Lumpur. If you consider to book this British Airways deal please look for flights mainly between second half of February and in March 2017. Max stay 12 months. This promotional sale is valid for bookings made till 8th of February 2017. Blackout period around Easter holidays as usually..
Booking samples - based on Skyscanner UK
London - Kuala Lumpur from £348 (British Airways non-stop flight)
London - Singapore from £366 (British Airways non-stop flight)
Travel date samples from Barcelona
21.2. - 13.3.
7 - 21.3.
9. - 23.3
10. - 27.3.
16.3. - 3.4.
21.33. - 6.4.
27.3. - 26.4.
Once you reach South East Asia you have full scope of possibilities where to accommodate. If you still want to book your hotel in Kuala Lumpur and/or Singapore in advance you may check some affordable accommodation via booking agents such as Booking.com.
Booking sample of a cheap open jaw flights to Kuala Lumpur/Singapore £259/€303 here. In this case you would be departing from Barcelona to Singapore on 10th of March. You would be then returning back from Kuala Lumpur to London on 27th of March 2017.