The short answer is ‘no.’
Once the freehold purchase process has started under the 1993 Act (the Leasehold Reform Housing and Urban Development Act 1993 [as amended]) there is no statutory provision whatsoever requiring those participating to admit any other flat owner in the building to their number.
Similarly, under the 1987 Act (the Landlord and Tenant Act 1987), once the acceptance notice has been served there is no requirement for the qualifying majority to admit any newcomers.
In practice newcomers are often welcome, as they may assist in sharing the overall cost of the process but there is no requirement as the law currently stands to admit anyone who was not part of the original process.
Therefore if the freehold to your building is being offered to you – or you are considering taking control of the process by serving Notice on your landlord, you should consider this point (among other factors) when deciding whether to join in or not.