Problems serving SVN over HTTPS on Ubuntu 10.04

We've been experiencing some problems with our Subversion server after upgrading to Ubuntu 10.04. When trying to access a repository, regardless of client (I've tried git-svn and svn on Windows as well as svn on Ubuntu 10.04, from different computers and network locations), I get a 400 bad request. Here's the output from svn:

svn: Server sent unexpected return value (400 Bad Request) in response to
     OPTIONS request for 'https://svn.example.org/svn/programs'

Here are the relevant entries from the Apache logs (I'm running Apache 2.2):

error.log

[Mon Jun 14 11:29:31 2010] [error] [client x.x.x.x] 
                           request failed: error reading the headers

ssl_access.log

x.x.x.x - - [14/Jun/2010:11:29:28 +0200] "OPTIONS /svn/programs HTTP/1.1" 
            401 2643 "-" "SVN/1.6.6 (r40053) neon/0.29.0"
x.x.x.x - - [14/Jun/2010:11:29:31 +0200] "ction-set/></D:options>OPTIONS 
            /svn/programs HTTP/1.1" 400 644 "-" "SVN/1.6.6 (r40053)
            neon/0.29.0"

If anyone has run into similar problems or could give me a pointer to track down the cause of this I'd be very grateful - I'd really like to avoid having to downgrade the box again.

Edit 2010-09-30:

There's a proposed fix in lucid-proposed now, apache2 2.2.14-5ubuntu8.3. See the bug report link in the accepted answer for details.