Finally I got it!
What you can do is this:
Initiate your request using UIWebView as normal. Then - in webView:shouldStartLoadWithRequest - we reply NO, and instead start an NSURLConnection with the same request. 
Using NSURLConnection, you can communicate with a self-signed server, as we have the ability to control the authentication through the extra delegate methods which are not available to a UIWebView. So using connection:didReceiveAuthenticationChallenge we can authenticate against the self signed server. 
Then, in connection:didReceiveData, we cancel the NSURLConnection request, and start the same request again using UIWebView - which will work now, because we've already got through the server authentication :)
Here are the relevant code snippets below.
Note: Instance variables you will see are of the following type: 
UIWebView *_web
NSURLConnection *_urlConnection
NSURLRequest *_request
(I use an instance var for _request as in my case it's a POST with lots of login details, but you could change to use the request passed in as arguments to the methods if you needed.)
#pragma mark - Webview delegate
// Note: This method is particularly important. As the server is using a self signed certificate,
// we cannot use just UIWebView - as it doesn't allow for using self-certs. Instead, we stop the
// request in this method below, create an NSURLConnection (which can allow self-certs via the delegate methods
// which UIWebView does not have), authenticate using NSURLConnection, then use another UIWebView to complete
// the loading and viewing of the page. See connection:didReceiveAuthenticationChallenge to see how this works.
- (BOOL)webView:(UIWebView *)webView shouldStartLoadWithRequest:(NSURLRequest *)request navigationType:(UIWebViewNavigationType)navigationType;
{
    NSLog(@"Did start loading: %@ auth:%d", [[request URL] absoluteString], _authenticated);
    if (!_authenticated) {
        _authenticated = NO;
        _urlConnection = [[NSURLConnection alloc] initWithRequest:_request delegate:self];
        [_urlConnection start];
        return NO;
    }
    return YES;
}
#pragma mark - NURLConnection delegate
- (void)connection:(NSURLConnection *)connection didReceiveAuthenticationChallenge:(NSURLAuthenticationChallenge *)challenge;
{
    NSLog(@"WebController Got auth challange via NSURLConnection");
    if ([challenge previousFailureCount] == 0)
    {
        _authenticated = YES;
        NSURLCredential *credential = [NSURLCredential credentialForTrust:challenge.protectionSpace.serverTrust];
        [challenge.sender useCredential:credential forAuthenticationChallenge:challenge];
    } else
    {
        [[challenge sender] cancelAuthenticationChallenge:challenge];
    }
}
- (void)connection:(NSURLConnection *)connection didReceiveResponse:(NSURLResponse *)response;
{
    NSLog(@"WebController received response via NSURLConnection");
    // remake a webview call now that authentication has passed ok.
    _authenticated = YES;
    [_web loadRequest:_request];
    // Cancel the URL connection otherwise we double up (webview + url connection, same url = no good!)
    [_urlConnection cancel];
}
// We use this method is to accept an untrusted site which unfortunately we need to do, as our PVM servers are self signed.
- (BOOL)connection:(NSURLConnection *)connection canAuthenticateAgainstProtectionSpace:(NSURLProtectionSpace *)protectionSpace
{
    return [protectionSpace.authenticationMethod isEqualToString:NSURLAuthenticationMethodServerTrust];
}
I hope this helps others with the same issue I was having!