Simple answer - yes, and you can reclaim your costs just as you could reclaim the mileage if you were using your private car. In fact you don't need to worry about the cost sharing aspect if in effect your company is re-imbursing you for the cost of the flight as if you had been making it on your own/in your private vehicle.
Legal gobbldeygook follows
Costs sharing Article 160
A flight will be a private flight if the valuable consideration falls within 157(3)(c), or relates to a group owned aircraft under 162 (3) or is a contribution to the direct costs of the flight otherwise payable by the pilot in command. The further criteria that apply are that no more than 4 persons (including the pilot) are carried, that the proportion that the contribution bears to the direct operating costs does not exceed the proportion which the number of persons carried on the flight (excluding the pilot) bears to the number of persons carried (including the pilot), i.e. where 3 people are on the flight two thirds and where there are 4, three-quarters. Further, no information can be published or advertised prior to the flight except in the case of an aircraft operated by a flying club in which case there can be advertising wholly within the premises of the flying club and all of those carried must be over 18 and club members. The operator of the aircraft being flown cannot employ the pilot of such a flight directly or indirectly. In respect of a payment made or promised for aircraft hire under 157(3)(c) the airworthiness requirements of part 3 to the ANO will apply as for a public transport flight.
Recovery of direct costs Article 161
This allows an aircraft to be used for work purposes in the same way that a mileage allowance in a car would be repayable as expenses. Article 161 provides that a flight will be a private flight if the valuable consideration is made other than under article 157(3)(c) and 162(3) and is payment in whole or in part of the direct costs of the flight otherwise payable by the pilot in command made by his employer or by or on behalf of a company of which the pilot is a director provided that neither the pilot in command nor any other person who is carried is legally obliged whether under contract or otherwise to be carried. Thus you can opt to use a light aircraft for business but your employer cannot force you to.
As with the other exemptions, payment in respect of aircraft hire for business purposes will not exempt the aircraft from complying with the public transport requirements of the airworthiness part to the ANO. Thus a company owned aircraft or a private aircraft can be operated on a private C of A but an aircraft hired for business purposes will require a public transport C of A.