What's a perfect 2-day itinerary in London, UK?
Cheapest option would be to get from Stansted Airport to Liverpool Station.
Liverpool station is located right in the city of London, near famous Gherkin tower.

From there you can rent a bike and take a view from Shard.

After the view from Shard - just bike to Big Ben and famous London Eye.

From Big Ben, it's quote close to Buckingham Palace.

See more photos here:
https://www.museuly.com/blog/20-london-photos-that-will-inspire-you/