You can always replace only the broken spokes, it's not like it's impossible in any way. However, spoke breakage is often due to spokes being fatigued due to being poorly tensioned originally. This means that the remaining life in the other spokes is questionable at best. Still, if you ca deal with spoke keeping popping every now and then it's certainly doable.
The sensible advise for a reliable ride OTOH is to replace them all. If the rim is worn, or if you want another one, this is a good opportunity. As bigdaddy suggests, alloy rims offer better braking if you're using rim brakes. Still, braking would improve more if you replaced the front rim.
Assuming you can keep the rim, a relace(spokes + labor) shouldn't be 60£, not even in London.
THen again, if the rim is OK it can be relaced with new spokes. Plenty of posters here who've tackled that by themselves. It is possible to replace them one by one, although it is tedious and more time consuming that doing it all in one go. For many rookie mechanics that approach feels less daunting. Being an IGH hub you either already have clearance for spoke replacement, or the sprocket will be very easy to remove.