Fatal error: Allowed memory size HELP

[#1]

Hi
This morning I tried to load a WordPress plug-in to backup my WordPress blog, which is embedded in my PlusNet hosted website.
The plug-in was UpdraftPlus. The plug-in didn't load and the website immediately came back with the error message:

Fatal error: Allowed memory size of 262144 bytes exhausted (tried to allocate 77824 bytes) in /share/storage/01/ex/expertek/blog/wp-includes/pluggable.php on line 354
Now that's all I get when I go to my website!
1 I've checked using FTP and the plug-in didn't load.
2 PlusNet say that the error means it's running out of memory, not diskspace and that it's a WordPress problem and they won't help. And I can't buy extra memory.
3 Changing the name of the pluggable.php file to pluggable2.php does not appear to change the error message!
How do I get my website back up and running!

[#2]

There is a memory limit in your php ini, or in the configuration setting which is now being exceeded when you try and load your site.
Try working out how to deregister the plugin through your database.  This might help:
http://blog.projectnibble.org/2011/07/22/quickly-disable-a-wordpress-plugin-via-the-database/