You would need to look at the specific fare rules to see what the options are, but here is my spin on it.

Y is fully refundable and changeable, with little or no extra costs for making those changes. On the SIN route, if you are buying in the last few days you will be forced to buy an expensive Y ticket because that is all BA will sell. The aircraft is nearly full and doubtless they are watching Singapore Airlines prices too. Market forces. Y fares to SIN return can be as low as £1800 or twice that.

B and H are semi flexible. They can be changed for a fee of typically £100. H typically is not refundable and many Bs aren't refundable. However if you make a change at the last minute you may end up paying Y - see previous paragraph - plus the £100. Best case scenario is that H is still available to it's just the £100, if B is still around and you have a H ticket then you may be looking at £200. Again it depends on the fare rules. On this route H may be £1100, B £1250 return.

With an L fare, the cost is nearer £850 return, and no refunds for cancellation. BUT this ticket may well be changeable for the £100. So I don't see the point in a B or H ticket if L is available. You won't get as many TPs or Avios obviously, and you would have to accept that any late change is going to cost a lot, but an early change would be possible to £100 or so. Note if the L fare goes up at the time of rebooking you'd also have to pay that.

So unless the change potential is extremely high, L is not a bad option.