I'm from the US where baptism when older is more common then christening as a baby except among Catholics. My sister and I however were christened as babies despite not being Catholic.
My husband is Catholic though not particularly religious but we decided early on in our relationship to raise our kids Catholic if we had any.
It's very important to me to have our daughter christened for religious reasons. To me a christening is a private, sacred, religious ceremony but in the UK it seems to have a huge social aspect attached to it that I'm not interested in.
Not only are we not interested in a big to do about it we can't afford the pomp and circumstance of invites, party, or dinner out for people. We live in a 1 bedroom flat without a garden...we don't even have room for a table so can't host it here. Plus most are 2.5 hours away.
My family wouldn't be able to come, her grandfather and his family wouldn't come because of my husband's Mum. So it would mostly just be his Mum there being over the top and annoying. 
So would we be unreasonable not to invite anyone and probably not tell anyone we had it done?