One problem is that you are UK and I am speaking as an American about American denominations. Still in all, there connections across the Atlantic are many.
The Unitarians immediately come to mind. They've merged with the Universalists into the Unitarian Universalist Assn. Also, there are certain branches of the Quakers (Society of Friends). Among the more mainline churches, the most obvious choice would be the United Church of Christ, formerly known as the Congregationalists.
And then there are the Methodists. Methodism might or might not work for you, but the famous appeal of John Wesley and Methodism is to live like a Christian ought, which accounts for their great emphasis upon peace advocacy, work among the homeless, hospitals and similar institutions, education, etc. etc.
There are also some smaller religious groups like the Swedenborgians and Ethical Science. All have the emphases I think you want. How to join varies from one to another, but some, such as the Unitarians, are as easy as can be in that area. Just inquire.
Yes, but he also taught about--and commanded in some cases--matters that you dismissed as tradition and custom only. Baptism, for instance. Reception of the Lord's Supper, study in the Scriptures, and so on.