According to a BBC News report in 1970,[12] it was determined that if the wreck of Richard Montgomery exploded, it would throw a 300 metres (980 feet)-wide column of water and debris nearly 3,000 metres (9,800 feet) into the air and generate a wave 5 metres (16 feet) high. Almost every window in Sheerness (population circa 20,000) would be broken and buildings would be damaged by the blast
It would damage buildings and shatter every window in town. Look up videos of the Beirut explosion to gain a sense of the amount of energy involved. Even with water as a shield the force and shockwave will still inflict harm.
(1) the UK doesn't have Tsunami warnings, because it doesn't have Tsunamis. This also means they don't know how to deal with them institutionally.
(2) Right by a river leading directly into the capital. I don't know how far away a 2m tsunami would actually go, is it close enough to the river entrance to focus it? https://www.floodmap.net to play with what "2m" would mean to the local area.