The rest are minor.
Nothing in Manchester
Land in london, spend time with relative in Hull. Return to London, Museum are free and British Museum is a must. Take the train to Paris and London. 2 days minimum in Paris and make sure you work out the agenda as everything is close to each other. After Amsterdam either return by train or ferry via English Channel to London. Still got time do outer London such as Oxford, strafford upon avon, stonehenge and even Bath.
Very important - accommodation in summer is critically short and very expensive, so book early. Especially Paris.