Cheap options to divorce?

Me and my wife have been married for almost 6 years but we separated last year in June due to constant arguments and basically fallen out of love with each other. We're both now seeing other people and I believe it's now the right time to file for a diverse.

Firstly where/how do I start this process? And do I need to pay out £550 to the government? Are there cheaper ways to do this especially since we both want this and have no ties (Kids, mortgage)