Its a complex question Britain was active in the sense they had to convince the US to go through the UN, which fell apart when the French said they'd veto anything. That meant we worked with US to build the ultimately flawed case for war as we committed to support them. Philosophically Blair saw Britain as the bridge between US and the EU and at the time thought to not support the US would cause irrepable political harm. Add in Hussein literally committing genocide totalling in 250,000 deaths and the fact the intelligence community thought he had WMD (flawed intelligence of a huge magitude but they genuinely thought theyd find it) the case for his removal wasn't high. The complete **** up was post invasion planning more than anything else.
I just have an issue with an idea Blair was warmonger who deliberately went to out to kill arabs rather than a guy who made an awful set of decisions with good intent that any other PM would not of made. He wasn't a saint either as he could of taken the French approach. But its a middle ground between the two rather than "should locked up in the hague", "only made a minor mistake".