When I meet with my clients I always ask them what their preference is for mourners to wear. Often they haven't even thought about it, or aren't aware that there are options available.
I encourage them to think about the person they are saying goodbye too, and what would be appropriate. For some people the traditional black of mourning is exactly what they want, but more and more nowadays people are choosing smart casual clothing. It may be that there is a favourite colour that is being used for the flowers and everyone can be asked to wear an item of that colour, or maybe team shirts or a uniform are more appropriate.
It is important for those attending to know what the dress code is; after all no one wants to turn up in black if everyone else is in smart casual with yellow as a theme. This means that the family have to make that decision and let everyone know.
As a Celebrant I am led by my clients. On a wet day standing at a graveside then navy or black smart trousers and sensible shoes is generally the way to go, but otherwise I tend to opt for a navy dress and jacket and smart shoes (my knees don't thank me, but I always prefer heels). Of course I have a black dress and jacket too, or I can wear a skirt and jacket with a bright top if that is what the client prefers.
It is easy to accessorise an outfit to add a splash of colour, if that is what is required. A tie for the men or a brooch or scarf for the females is an easy way to incorporate the favourite colour (football team colours etc) of the person you are saying goodbye too.
For those with long hair bear in mind how windy crematoriums and cemetery's can be. Mine is always in a bun and hair-sprayed until it won't move at all.
In my experience no client would ever wish for people to go out and buy a new outfit. Unlike a wedding, where buying a new dress or shirt is part of the occasion, a funeral is more of an occasion for wearing something you are comfortable in (apart from me and my heels that is)!
It is best to avoid white (unless specifically requested), and in most cases jeans are frowned upon, although they are becoming more accepted.
If you have been asked to speak, or carry the coffin (a pall bearer), then it is always best to check with the family to see what they would prefer you to wear. If you are a pall bearer then you will probably want to look similar to the other pall bearers (and the padded shoulder of a jacket is a good choice to protect your shoulder).
My top tip would be to have a pocket for a tissue or two and somewhere to put your donation, which is usually placed in a bowl as you leave. (Phones are best left in the car, otherwise make sure they are turned off).
What you wear to a funeral will always be led by the family. If you aren't sure then ask. If you don't want to bother the family then ask the Funeral Director. They will check with the family and let you know. If in doubt wear something dark and smart, with pockets!