This is quite a complicated matter, so I can't give definite answers but can give you some useful information. There is no such thing as custody now. When parents separate/divorce they can make whatever arrangements for their children they wish. However if there is a disagreement, the matter goes to the Family Court and one or other of them is granted a Residence Order (meaning that is where the child has his/her permanent home) and the other parent is almost always granted contact (the term access is no longer used)
I don't of course know what arrangements (if any) have been made between the parents of the children. How can you be sure that the father does not want to have the children live with him on a permanent basis. You also mention that he would need "some sort of access" - I think before you go any further the father of the children needs to be involved in plans for the children following the death of their mother. If your friend and the children's father were married he will have parental responsibility (PR) for the children as it is shared equally between a married couple. Even if they were not married in certain circumstances he could have PR or could be granted PR by the courts.
In any event your friend could not make any arrangements on a legal basis for the care of the children without consultation (and agreement or otherwise) for her proposals for the permanent care of the children. Making a Will does not mean that the father's rights can be over-ridden.
The difference between fostering and legal guardianship. Fostering means that the LA place the child with approved foster carers and they retain the PR and the carers are looking after the children on the LA's behalf, hence the legal term Looked Aftered Children.
Guardianship - the legal route is via a Special Guardianship Order (SGO) and normally social workers for Children's Services have to be involved because they have to assess the suitability of the applicants and complete a lengthy report that goes to court for the Judge's decision. However this is in cases where the children are already being looked after by the LA, which is not the case with these children. I'm honestly not sure what would need to happen if the mother and father agree that their children should have their permanent home with you until they are adults. SGOs give the applicants PR with 3 exceptions: 1. They are not allowed the change the child's surname without the consent of the birthparents. 2. They are not allowed to take the child out of the country for more than 3 months, nor apply for an Adoption Order without the consent of the parents.
Residence Orders. Since SGOs became the legal route to permanency ROs do not provide the same level of security for the child's future, because the PR is shared between the holders of the RO and the birthparents, and this can be problematic. Also the birthparents can return to court to request that the children be returned to them. LAs are keen on ROs because there is no need for lengthy reports and if there is agreement between you and both parents, then it would I think be a relatively simple matter to obtain a RO through the courts. IF you and the children's father were on good terms and the mother agreed, then a RO might be the best way forward, but it doesn't seem like this is the case.
Private fostering: If a child is cared for by a non-relative for a period in excess of 28 days they are meant to register with their local Social Services Dept., as private foster carers, the LA have a duty to assess the suitability (or otherwise) of the private foster carers.
I don't know how old or how many children are involved, but are you certain that you can care for these children throughout their childhood and remain a "family of resource" for them (as good parents would) throughout their adulthood. I don't know about your financial situation, but you would not be entitled to funding from the LA and so presumably would only have the Child Benefit - is this enough for you to care for the children.
Sorry I can't give you a definitive answer but it would be a good idea to talk to the local SSD and get advice and information. There are websites where you might get advice "British Agencies for Fostering & Adoption" (BAAF) and Fostering Network (the regional association for foster carers) There is a Children's Legal Centre but I can't remember the website address, but you need to do some googling and I'm sure you will find it.
I am assuming you don't want solicitors involved because of the costs. You might be aware that Legal Aid is no longer available for private law cases, such as this one, so you could have fairly hefty legal bills. If finance is not an issue then a suitably qualified lawyer in Family Law could probably give good advice as to the way forward.