Visiting London and Paris

So my fiancé and I are traveling to London and Paris in mid June. Our flight lands in LHR at 10:55 AM. Since we are only spending a day in Paris we decided to knock it out the same day we arrive to hopefully make the most of our trip. We booked the Eurostar to Paris with our designated arrival time being 4:16 PM in order to catch the train. Is that enough time to get from Heathrow to London St Pancras Intl? We tend to sometimes over pack our suitcases which leads me to my next question. How difficult is it traveling through London and Paris with luggage? We considered checking into our hotel in London a day early to drop our bags but would love to spend the extra money elsewhere if feasible. Any advice or feedback is greatly appreciated.