One possibility might be the cafe at Central Hall, a meetings and events venue, (but not the modern QEII Centre in the same area), literally across the road from the Abbey and on the way to the War Rooms. Or the Westminster Arms next door if a pub is an option.
But to guarantee quick and easy, if it’s a sunny day, buy some sandwiches or other picnic food and sit in St James’s Park, across the road from the War Rooms. There is also a cafe in the Park.