Madame Tussauds London doesn't provide lockers onsite, but does have a cloakroom facility located at Door Number 6 where items including coats, bags and pushchairs can be stored during your visit.
Prices to use this facility vary however below is an indication of the charges (please note this is subject to change):
Coats - £2
Small Bag - £3
Large Bag - £5
Extra Large Bag - £6
Umbrella - £1
Buggies/Pushchair - Free