[NumLock]

Вызывай UrlMkSetSessionOption до вызова URLDownloadToFile:

Код:

var
  s: String;
begin
  s:='Mozilla/5.0 (Windows NT 10.0; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/51.0.2704.84 Safari/537.36 OPR/38.0.2220.31';
  if UrlMkSetSessionOption(URLMON_OPTION_USERAGENT, @s[1], Length(s), 0)<>S_OK then raise Exception.Create('Oops');
  if URLDownloadToFile(nil, 'https://vk.com/s.kalaeva', 'kalaeva.htm', 0, nil)<>S_OK then raise Exception.Create('Oops');
end;