Am I wrong?

wrong. You need to increase to counterbalance what sh*tstorm that is ineviably approaching for the PRS and costs that this will involve. EPC upgrades, eviction costs...you NEVER know what is going to happen so why leave it to chance?

Should I mention you are running this as a business or do you see this as charity work??

You are doing your own tenant a disservice if you keep them believing that this status can go on forever. At some point you will have to raise the rent so start sooner rather than later.

It's not wrong to want to run a property more for social benefit or charitable purposes than commercial ones, but you should understand that this is what you are doing. It will also be at odds with the way you and the property are treated by HMRC, the Council, the law, maintenance workers etc, who will assume you are running it as a business. It will also mean that your tenant will never be able to afford to move and may miss opportunities and feel stuck. They may end up resenting you and feeling entitled to your charity. Others have reported exactly this.

Letting is a business not a charity
There are loads of Landlords on here moaning because they went down this path

I made that mistake. I didn't increase the rent for five years for great tenants until interest rates hit the fan this year and I had no choice. The problem was that the necessary rent increase was a hell of a jump. Had I increased the rents every year by 5% it wouldn't have been such a jump, making me look like a greedy landlord. Bad management on my part.

The 'Mistake' here was to not increase the rent on a regular basis. It does not have to be in line with inflation, a good tenant is somebody worth keeping, but to set the precedent that increases are a fact of life is useful.

As for what to do now, I'd schedule a sit down meeting and layout your costs, (mortgage increase etc), current rents in the area and so forth, then negotiate a mutually acceptable increase for the coming year. Further down the line implement regular increases.

Tenants are not unaware of the issues that are causing the rent increases. Personally I'm happy to rent out at below market rates if I have good tenants that I want to keep.

You might like to consider a rent reduction for the winter months to help with energy costs if they accept a higher rate over all. It can sweeten the pill.

as Julia Roberts said " big, big mistake"!

Ouch….
I’m assuming it’s paid for else you would have increased long time ago…
Needs a ‘fair increase’ difference £400 pcm is £4800 PA
In my opinion a lot of money in real terms as would probably take care of your gas and electric bills ….
I would be asking for an increase and if they leave you fill easily at £600/700 /800 pcm
Speak to them nicely and I’m sure they will oblige equally.

My thoughts on this, for what they are worth, is to remember that the decision that you make will directly impact the livelihood and wellbeing of another person, with no choice in that being made by the other person.

You may have to decide if you are raising the rent because you need to, or if you are raising the rent because you can. The latter looks horrible to the wider population and looks like money grabbing. If you need to raise the rent because your expenses have gone up, then by all means raise it. If you do need to raise the rent for this reason, meet with the tenant, tell them how your costs have gone up and give examples. Saying "Increased government regulation" or "Market Rent levels" feels wishy washy and vague.

We tenants are not stupid. We are also very aware when we are paying less than we could be. We will act accordingly if we are shown compassion from our landlords.

Raising the rent could mean resentment. It could be that all those little maintenance jobs that are done by the tenant now result in phone calls to you regularly. It could mean that they seek out alternative accommodation and you get an unknown tenant into the property while someone else gets your reliable tenant instead.

Finally, I keep seeing the phrase "you are a business, not a charity". My first paragraph aside, my other thought on this comment is that if landlords keep saying they are a business and don't show compassion, do not be surprised when the government starts treating you exactly like a business.

Like you I did the same for 3 years but then decided to bite the bullet and increase the rent by a small amount.
I contacted my tenant for a chat, went round and she looked really worried. I said I wish to increase the rent a little and she was delighted. She initially though I was going to ask her to leave. She had looked around and there was nothing she could afford, hence the worry.
It is good for the tenant to expect say an annual increase, even if its just by a very small amount.
If you don't do this then you are robbing yourself. Go online with a compound calculator and look at how much that has cost you over 10 years- make sure you are sitting down when you do this. It also gives the tenant an unrealistic impression of what the local rental market is like.

When you come to sell, if you do, having a well below market rent will not help you with CGT liability.

What is the Local Housing Allowance? https://lha-direct.voa.gov.uk/Search.aspx

I would increase the rent at least £100pm for this year, then see where you need to be next year.

You have increasing buildings insurance; increasing Gas Safety Certificates; likely renewing EICR at some point, general maintenance costs increasing