Menzies is very strong and by far the biggest handler at LHR but yes everywhere else they seem to be losing contracts right left and centre...the ground handling market in UK is becoming very fragmented with smaller companies entering (Stobart, Azzurra, Premier Handling etc) still think Dnata is the one to watch... a big global player with very deep pockets.
Several times MAN has gone from multiple Handling agents to only a few with near monopolies and back again. Neither seem to work well. When there are multiple handling agents, each one has to hire/buy equipment/staff/rent office space etc... and with out the economies of scale (Airlines will only pay crumbs these days), they struggle to make any return on investment. When there are near monopolies (Swissport/Menzies), the handling agents struggle to cope with the volume of work and just end up giving a very poor service. High staff turnover/Lack of training/poor equipment/low pay/ lack of suitable crew rest areas... I could go on are the norm these days outside of LHR.
Dnata at MAN have so far offered little. They even got an improvement notice from one of their customers once, I think they were called Emirates !