Removing a middle name by deed poll is just as valid as adding one. There are many reasons people choose to drop a middle name — it may be a name they have always disliked, one that is associated with difficult memories, one that creates confusion because it is close to their first name or surname, or simply one they have never used and do not want to carry on their legal documents. Whatever your reason, you have the absolute right to remove it.
The process is straightforward. Your deed poll states your current full legal name — including the middle name you are removing — and your new full legal name without it. Once signed by you and two adult witnesses, the document is valid. You then present it to each organisation that holds your records to have them update the name on their systems.
A deed poll that removes a middle name should be clear about exactly what is changing. If your current name is Jane Elizabeth Smith and you want to remove "Elizabeth", your deed poll states that you are abandoning the name Jane Elizabeth Smith and intend to be known as Jane Smith. The clarity of the before-and-after statement is what makes the deed poll easy for organisations to process.
As with adding a middle name, different organisations treat middle names differently. The Passport Office records and displays middle names — removing one will result in your new passport showing your name without it. The DVLA and many banks may not record middle names at all, so for those organisations the change may already reflect the situation on their records. Updating the Passport Office is typically the most impactful step if you want your primary ID documents to reflect the removal.
There is no need to explain why you are removing a middle name. Your reasons are private. The deed poll does not include a field for motivation, and no organisation that processes the change will ask you to explain it.