Sure, here's a detailed itinerary for your first day in London, 4/29:
7:15 am: Arrival at LHR airport.
9:00 am - 10:30 am: After customs and immigration procedures, take the Heathrow Express train to Paddington Station. From Paddington Station, take the Bakerloo line to Regent’s Park station, which is the nearest station to Queen's Rose Garden.
10:30 am - 12:30 pm: Visit Queen's Rose Garden, which is located in Regent's Park. The garden has over 12,000 roses of 85 varieties. You can enjoy the beautiful flowers, take pictures and relax in the peaceful environment.
12:30 pm - 1:30 pm: Have lunch around Regent’s Park or head to nearby Camden Market for a wide variety of food options.