London PE Recruitment

Currently a consulting analyst working at a boutique firm specializing in pharma/biotech. Most of the work I have done revolves around commercial strategy (i.e., market sizing, revenue/demand forecasting, go-to-market, new product planning). At this stage, I want to try and transition to a PE/VC role in a fund that invests in the pharma/biotech space. From speaking to a couple of people who made the transition, I gather my best shot would be to reach out to recruitment firms that specialize in PE/VC recruitment in London and provide an updated copy of my resume. Are there any particular funds that specialize primarily in pharma/biotech investments? Are there any specific recruiters that work in this space more so than others? Does cold emailing recruiters on Linkedin usually work or is a more ''formal'' approach preferred?

Appreciate most consultants who exit to PE/VC come from MBB/Tier 2 firms, so would also appreciate any piece of advice to boost my chances when trying to lateral!