Peel Hunt - what do they actually do?

Sure so generally considered an OK-Good mid/low cap IB within the UK targeting mostly companies on the LSE AIM (basically too small to get listed on the main LSE). 

If you want a better picture of what they do google what is a corporate broker UK / use WSO to find it, there are a good couple posts about it but it boils down to leveraging existing relationships to gain M&A and ECM deals. I'm not sure % breakdown but as with most lower/mid cap IB in London I would assume its mostly ECM, this will be a combination of IPO, secondary transactions etc however I know PH has a dedicated M&A team so likely somewhat active but still a lower emphasis. 

Peel Hunt maintain / win their corporate broking relationships mostly through their ER, in fact some of their clients will likely only be covered by PH as considered too small for other banks to bother with (this applies to a lot of companies on AIM not just PH clients). Look to understand the relationship between ER, Corporate Brokers and firms like I've listed above and you'll be good to go, main competitors include Numis, Investec, Berenberg(?), and to a lesser extent firms like singer

General point about the space is the last year was shit but this year hasn't started as terrible as people feared but still not great - research who the person you are meeting and the deals PH has done in that space and you should be good to go