We moved from the UK to Dubai and used Bournes Removals. They were excellent to deal with in the UK - the guy came and did a survey for shipping. Their quote was competitive, the packing team were superb, they were on time, they knew what they were doing, they packed the container and even added some extra stuff that I decided right at the last minute that I could not live without! They stuck to their estimated time for packing and wrapped and packed professionally. The container arrived at the docks here in Dubai earlier than they estimated and the team at the Dubai end were just as professional.
I would highly highly recommend them. We had a 40ft container I think and with all the stuff they packed we had one cheap Ikea glass break! Everything else was in tip top condition.
I know others who have since used them and have been equally happy. the other international movers who are also highly recommended here in Dubai are Allied Pickfords and Crown Relocations.
www.bournes-uts.co.uk Not sure if they service cheshire but they are part of the UTS group so am pretty sure they would cover cheshire through their networks.
Hope that helps - happy moving!