It's just happened again, although I didn't get the high pings afterwards; this time I was able to get some traceroutes. I had to tracert to an IP address and use -d because nothing would resolve:
At 7.30 this morning (1st hop is my router):
1 * * * Request timed out.
2 14 ms 14 ms 14 ms 212.69.63.45
3 * * * Request timed out.
4 * * * Request timed out.
5 * * * Request timed out.
6 * * * Request timed out.
How it looks if it's working:
1 * * * Request timed out.
2 15 ms 15 ms 14 ms 212.69.63.45
3 16 ms 15 ms 15 ms 212.69.63.9
4 16 ms 16 ms 15 ms 213.232.64.51
5 16 ms 19 ms 16 ms 213.206.128.104
6 16 ms 16 ms 15 ms 213.206.129.152
7 16 ms 16 ms 16 ms 213.206.131.22
8 16 ms 18 ms 16 ms 4.68.116.98
9 16 ms 16 ms 17 ms 4.68.128.110
10 16 ms 16 ms 17 ms 4.68.117.41
11 85 ms 85 ms 85 ms 195.50.116.154
12 88 ms 89 ms 87 ms <my office IP address>
Trace complete.
I've only been with IDNet for a month, but I've found the connection to be less stable than my previous f2s one. If this carries on I'll be seriously considering moving on again.