Been playing around with this....

The booking engine won't let you but you *can* go outbound WT+ and return J (by booking WT+ and selecting the upgrade option on the price quote page) which suggests the fares are combinable.

So I took a look at matrix.itasoftware.com and it looks OK:

London, United Kingdom to Singapore, Singapore: 6757 miles 12 hrs 55 min
British Airways British Airways Flight BA7372 on a Boeing 747 (jet) in business class
(operated by Qantas Airways as Flight QF32)
(lunch, refreshments)
Departs London, United Kingdom (LHR) Tue, May 12 12:15p 12 hrs 55 min
Arrives Singapore, Singapore (SIN) Wed, May 13 8:10a
1 adult in booking code I, covered by fare (A1) below
Note: The flight from London (LHR) to Singapore (SIN) is overnight.

Singapore, Singapore to London, United Kingdom: 6757 miles 13 hrs 15 min
British Airways British Airways Flight BA12 on a Boeing 747 (jet) in coach class
(meal)
Departs Singapore, Singapore (SIN) Wed, May 20 10:55p 13 hrs 15 min
Arrives London, United Kingdom (LHR) Thur, May 21 5:10a
1 adult in booking code N, covered by fare (A2) below
Note: The flight from Singapore (SIN) to London (LHR) is overnight.


Booking details
If you want to buy this ticket, contact the airline (British Airways: 1-800-247-9297, http://www.britishairways.com/) or a travel agent. If you use a travel agent to buy this ticket:

* If your travel agent is online and has an e-mail address, e-mail this itinerary to them
* If your travel agent is not online, print out this page and fax/give it to them

It is very important to use exactly the same booking codes and fare codes that we've used on this page in order to match the price we've found.

Fare (A1): BA LONSIN IAPUK2 fare (rules) £641.50
Fare (A2): BA SINLON NLRCUK9 fare (rules) £183.50
Tax: United Kingdom Air Passengers Duty £80.00
Tax: United Kingdom Passenger Service Charge £21.20
Tax: BA YQ surcharge £169.00
Tax: Singapore Passenger Service and Security Charge SGD 28
Total for 1 adult passenger: £1108.20

Fare construction (sometimes useful to travel agents):
LON BA SIN M 945.45IAPUK2 BA LON 270.44NLRCUK9 NUC 1215.89 END ROE 0.678509 FARE GBP 825.00 XT 80.00GB 21.20UB 13.00SG 169.00YQ