Most churches in the UK are set up as charitable trusts. There are a number of ways to do this but increasingly, the most common is as a Charitable Incorporated Organisation. This then raises the question of who should serve as trustees for the church.
There seem to be three main options that churches run with. One option is for all of church office holders to serve as trustees. So, if your church has elders and deacons, then all elders and deacons are also trustees. A second option is for the elders to be the trustees and the third option is for the non-elder leaders (often deacons) or a number of them to take on the role.
The reason why some churches appoint non-elders to the role of trustee is because this is perceived as a practical aspect of church life and if elders have spiritual oversight, then they do not want to be distracted from that by legal matters.
I’m not sure that this is the best way of approaching things. First of all because it creates a “spiritual/practical” dichotomy that I’m not convinced we find in those terms in Scripture. Secondly, because it may create the impression that there are two competing spheres of authority in the church. In fact, at my last church we had a hybrid solution where the trustees were appointed as a separate body to the elders but we always had two elders on the trustees to ensure that this body didn’t usurp the elders authority.
This perhaps reflects how the role of trustee actually is understood by the civil authorities outside of the church. For those authorities including the Charity Commission, and Inland Revenue, the trustees are those people they regard as responsible for the church, for its leadership and governance and for everything that the church does or happens on and to premises owned by it.
So, we might say that “elder” is the word given for those that Scripture, the Holy Spirit and the church internally recognise as all or some of the leaders of the church whereas “trustee” is the word used by those outside of the church to recognise who its leaders are.  For that reason, I think it is best if the two align. So, those recognised by Scripture, the church and the Holy Spirit should be the same as those recognised by the law of the land.
For that reason, my personal view is that all of those recognised by the local church as leaders including all elders and deacons should also be appointed as trustees.
 I say “all or some” because my understanding is that the leadership of the church in terms of setting its spiritual direction and ensuring there is pastoral care for the members is provided by a plurality of leaders. This includes elders who have specific teaching responsibility and the role of providing and protecting. Elders are male. However, I also believe that the overall leadership of the church is not just male and not just about elders but includes a plurality of men and women who are known to have gifts of wisdom and discernment.