。
She made the most of her stay in London to greatly improve her English.
Literal
[topic-は] London stay [object-を] making-use-of greatly English [genitive-の] power [object-を] extended.
活用する ('to make use of, apply') is a Sino-Japanese verb often paired with abstract resources — opportunities, knowledge, time. 大いに is a literary adverb meaning 'greatly, much' (it carries more weight than すごく or とても in writing). 英語の力 literally 'English's power' is the standard way of saying 'English ability' — 力 functions as a productive suffix for skill in any field: 学力 (academic ability), 体力 (physical strength), 想像力 (imagination). 伸ばす ('to extend, stretch') used metaphorically of a skill means 'develop, improve.'