Is anyone able to help me see if I can make my commute into London via train any cheaper?

[anonnamechange4]

I've tried to do some research but find it quite confusing, and wondered whether anyone has more experience or knowledge and is able to help.

I commute to Wood Lane, London via Richmond.

I take a direct train to Richmond on the Reading to Waterloo line, and then go Richmond to Hammersmith to Wood Lane. I go during rush hour (leaving at 7:30am in the morning and arriving by 9am, and leaving to go home at approx 5:30pm.

Last week's commute cost me £36.70 per day (£13.40 on the tubes, £23.30 on the train to Richmond). This seems quite steep but not sure if it's just normal

I pay by contactless on my card on the tube, and buy a ticket from South Western Railway for the train into Richmond. Would getting an Oyster card save me any money?

Thank you in advance

According to trainine if you do virg water to shep bush, changing at Clapham junction, an anytime day return is £19.60.
it think it’s better if you can avoid adding the tube cost to the train..

How often are you commuting? Usually a weekly/monthly/flexi season ticket for the train part is cheaper than paying at the station on the day.