Hazell has got some nice clobber on. Shoes from Bond Street. He aims to go up in the world.
When Gregory tells Hazell to forget any plans for a holiday. He ends up looking at social climber Jonathan Clayton. He claims to be a financier who is romancing 17 year old Sarah Courtney. When she turns 18 she will inherit a trust fund.
Her wealthy parents have hired Hazell as they think Clayton is more interested in their daughter's inheritance.
Hazell pretends to be a wealthy fruit and veg wide boy looking to invest money with Clayton. Hazell certainly discovers that Clayton has told a few fibs about himself, is a ladies man and has made a pile of cash. He genuinely seems to love Sarah but her mother has other ideas.
I am not sure Hazell works being upwardly mobile. That is Gregory's domain. I think the show does better when it is down and dirty in the back streets of Soho. This episode is basically one where not a lot happens but the upper classes do love a bit on the side.