I'm a major Barbour fan but for London travel in May the waxed jacket would stay at home. My choice instead for this time of year is Barbour Linehope Featherweight but sadly it is discontinued.

Barbour has a good line of non-wax lightweight jackets that are fashionable and rainproof. When you are in London you might want to consider a new one. There are stores around the city. My favourite is the location on Regent Street. Harrods has a good selection although often at a higher price. Remember you can reclaim the VAT upon departure.